THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 


Benno  Rubinyi 


A  COURSE  IN  THE  ANALYSIS  OF  THE  CHORDS  AND  OF 

THE  NON-HARMONIC  TONES  TO   BE   FOUND 

IN  MUSIC,  CLASSIC  AND  MODERN 


BY 


BENJAMIN   CUTTER 


BOSTON 

OLIVER    DITSON    COMPANY 


NEW  YORK 

CHAS.   H.  DITSON  &  CO. 


CHICAGO 

LYON  &  HEALY 


Music  L!bra«$ 


HARMONIC    ANALYSIS 


PREFACE. 


THIS  book  is  designed,  primarily,  for  those  who  have  studied 
Harmony  and  would  apply  it  in  their  every-day  musical  life, — 
in  other  words,  in  their  playing  and  in  their  teaching.  It  is 
planned  —  although  no  premium  is  hereby  placed  on  superfici- 
ality—  as  much  for  those  people  who  have  made  poor  work  of 
their  harmony,  so  far  as  turning  out  a  good-sounding  product  is 
concerned,  as  for  those  to  whom  the  difficulties  were  as  naught. 
Furthermore,  it  is  planned  for  him  who,  living  in  some  place  inac- 
cessible to  the  best  performances,  would  fain  review  what  he  has 
learned,  —  if  possible,  in  a  manner  other  than  that  of  laboriously 
writing  exercises,  —  would  broaden  his  musical  horizon  and  thus 
increase  the  gift  Heaven  has  given  him,  and  appease,  in  a  measure, 
that  hunger  for  chords  and  for  things  harmonic  which  characterizes 
so  strongly  this  present  day. 

By  not  a  few  observers  it  has  often  been  thought  that  the 
ordinary  course  in  harmony  ceased  before  its  rightful  end,  and 
that  there  was  no  connection,  or  not  enough  connection,  made  be- 
tween harmony  and  playing;  i.e.,  between  harmony  and  practical 
musicianship.  Harmonic  Analysis,  it  has  been  held,  would  give 
the  ordinary  non-composing  student  an  opportunity  to  make  his 
harmony  a  live  tiling;  and  experience  has  justified  this  idea. 

The  Course  of  Instruction  in  the  New  England  Conservatory 
of  Music,  Boston,  Massachusetts,  from  which  this  book  has  grown, 
was  planned  for  forty  class  lessons.  After  canvassing  the  field,  the 
following  representative  works  were  chosen,  and  have  been  held 
to  with  gratifying  success  :  Schumann,  $<-cncs  from  Childhood, 
Op.  68;  Bizet,  Suites.  JSArl'xicnni-.  Xos.  1  and  2  ;  Chopin,  7Vr/Mr7rs; 


vi  PREFACE. 

Wagner,  Selections  from  Tannhduser,  Lohengrin,  Tristan ;  and,  in 
some  cases,  Grieg,  Hunioresken,  Op.  6.  Absence  of  a  text-book 
made  imperative,  however,  from  the  beginning,  not  only  the  dicta- 
tion of  principles,  but  also  constant  discussion,  time-robbing,  and, 
because  more  or  less  was  naturally  forgotten,  unsatisfactory.  A 
text-book  became  necessary;  a  book  comprehensive  and  up  to  date. 
On  studying  his  subject  for  the  recitation  and  for  this  book,  the 
writer  confesses  that  he  was  dismayed  by  its  dimensions  and  by 
the  very  multitude  of  conditions  he  was  forced  to  consider  and  to 
explain.  The  number  of  harmonic  phenomena,  of  tone  combina- 
tions, complications,  which  occur  in  modern  music,  although  they 
admit  of  a  reasonable  classification,  goes  well-nigh  into  the  infinite. 
More  than  this,  not  a  few  are  extremely  subtle  in  nature.  Things 
which  the  composer  absorbs  unwittingly,  and  accounts  for  in  an 
oft-handed  manner,  if  at  all,  may  to  the  layman,  when  he  comes  to 
define  them,  present  very  considerable  difficulties.  Furthermore, 
these  subtleties  occur  in  -e very-day  modern  music.  For  these  rea- 
sons a  certain  breadth  of  scope  and  entrance  into  detail  has  been 
observed  from  necessity  in  the  general  plan  of  this  book. 

As  will  be  noted,  examples  have  been  drawn  from  the  most 
varied  sources.  The  page-limits  of  a  work  of  this  sort  forbade, 
however,  the  use  of  many  quotations  which  might  have  been  used 
and  which  suggest  themselves,  no  doubt,  to  the  connoisseur.  But 
it  is  thought  that  this  presentation  will  be  found  ample  enough  for 
practical  purposes, — -provided  the  student  applies  what  he  has 
acquired  here. 

It  is  believed  by  men  generally,  that  the  understanding  of  a  thing 
heightens  its  enjoyment.  We  read  "  Hamlet "  with  care,  that  not 
a  point  of  stage-craft  may  be  lost,  and  our  emotions  are  moved  the 
more  powerfully  because  of  our  knowledge.  In  the  same  way,  it  is 
believed  that  by  a  careful  study  of  this  book,  one  may  learn  not 
only  to  analyxe  and  to  understand  anything  in  the  way  of  har- 
mony that  he  may  chance  to  meet  in  musical  literature,  classical  or 
modern,  but  — what  is  far  more  important' — through  his  height- 
ened powers  of  comprehension  he  may  be  enabled  to  hear  with 
greater  understanding,  to  read  at  sight  with  more  facility,  to  play 


PREFACE.  vii 

and  to  sing  with  more  intelligence,  and  consequently  may  have 
his  musical  perceptions — those  gifts  of  delight  to  man  —  quick- 
ened and  made  more  responsive,  whether  he  aot  as  player,  as  singer, 
or  as  listener. 

And,  lastly, — and  this  is  not  the  least  consideration,  —  the  author 
believes,  and  by  experience  knows,  that  the  student  of  composition 
may  be  benefited  by  a  study  of  this  subject ;  that,  instead  of 
spending  more  or  less  valuable  time  in  finding  out  the  many 
minutite  of  modern  harmony,  he  may  behold  them  here  stated  for 
his  examination  and  possible  application. 

BE-N'JAMLNT    CUTTER. 
BOSTON,  June  12,  1902. 


CONTENTS. 


PART    ONE. 

INTRODUCTORY. 

SECTION  PAGE 

1.  DEFINITION 1 

2.  REQUIREMENTS 1 

3.  ON  PROGRESSIONS  IN  GENERAI 1 

4.  PLAN  OF  STUDY 2 

5.  REMARKS  TO  THE  TEACHER 2 

6.  SIGNS  USED  IN  MARKING 3 

7.  PRINCIPLES  OF  ANALYSIS.     (Preliminary  Statement.)     ...  4 

8.  TRIADS  AND  SEVENTH  CHORDS.     (No  Modulations.) .     ...  4 

9.  THE  BROKEN  CHORD 8 

10.  REDUCTION 9 

11.  THE  BROKEN  CHORD,  THE' APPOGGIATURA,  THE  PASSING  TONE, 

AND  THE  EMBELLISHMENT 10 

12.  MODULATION 15 

13.  PRINCIPLES  OF  ANALYSIS 17 

14.  REAL  MODULATIONS  .  19 


PART    TWO. 

TUP:    NON-HARMONIC   TONES,    IN    DETAIL. 

IT).     INFERENCES '23 

16.  THE  Ari'oGc.i.vruRA   (ci>iithtucd\ 23 

17.  THE  APPOGGIATURA  CHORD 25 

18.  THE  FREE  TONE  2G 


X-  CONTENTS. 

SECTION  PACK 

19.  THE  PASSING  TONK  (continued) 27 

20.  THK  EMBELLISHMENT   (continued) 28 

21.  THE  EMBELLISHING  CHORD 29 

22.  THE  SUSPENSION 31 

23.  THE  ANTICIPATION 33 

24.  THE  FREE  ANTICIPATION 34 

25.  THE  RETARDATION 34 

26.  THE  ORGAN  POINT  ;  THE  PEDAI 35 

27.  DISPERSION  OF  CHORD  MEMBERS ,     .     .     .  37 

28.  TONES  SUSTAINED  BY  DAMPER  PEDAL  OF  THE  PIANO     ...  38 

PART    THREE. 

MODULATION  IN   GENERAL,  THE   ALTKRKI)  CHORDS,  ETC. 

29.  ALTERED  CHORDS 

30.  THE  SUPERTONIC  SEVENTH  WITH  SHARP  THIRD    ...  .39 

31.  OTHER  ALTERED  STEPS 40 

32.  APPARENT  AND  REAL  MODULATIONS  .  41 

33.  CONSECUTIVE  DOMINANT  SEVENTHS 44 

34.  ENHARMONICS * 44 

35.  MODULATION  THROUGH  THE  Six-Fouit 49 

36.  ASSUMPTION  OF  KEY 49 

37.  INCOMPLETE  MODULATION ">0 

38.  THE  DECEPTIVE  RESOLUTION 

39.  PASSING  DIMINISHED  SEVENTH  CHORDS 

40.  THE  DIMINISHED  SEVENTH  ON  THE  RAISED  FOURTH  STEP  .  54 

41.  SECONDARY  SEVENTH  CHORDS  IN  GENERAL    .     . 

42.  THE  AUGMENTED  SIXTH  CHORDS °6 

43.  MODULATION  DOWN  A  MINOR  SECOND  BY  AN  AUGMENTED  CHORD  59 

44.  CHORDS  WITH    A    DIMINISHED  THIRD   OR    HIDDEN    AUGMENTED 

SIXTH 61 

45.  THE  FLAT  SECOND  AND  SIXTH  STEPS 61 


CONTENTS.  xi 

SECTION  pAGK 

46.  THE  FLAT  SEVENTH  STEP .  62 

47.  EMBELLISHMENT  OK  THE  TONIC  SIX-FOUR  IN  A  CADENCE     .     .  63 

48.  CONSECUTIVE  TONICS 64 

49.  CHROMATIC  PASSING  CHORDS  AND  PASSING  SEQUENTIAL  FIGURES  65 

50.  THE  SEQUENCE 68 

51.  Two  SIMULTANEOUS   HARMONIES 71 

52.  THE  SKIP  RESOLUTION 73 

53.  THE  CHURCH  MODES,   AND   UNUSUAL  CADENCES 75 

54.  TWO-PART  WRITING 76 

55.  ONE-PART  WRITING  AND  THE  CADENZA 77 

56.  REDUCTION  (continued) ;  ITS  APPLICATION  IN   MEMORIZING  AND 

IN  SIGHT  PLAYING 80 

57.  FULL  TABLE  OF  SIGNS 88 

58.  SPECIAL  REMARKS  TO  THE  TEACHER 89 

PART    FOUR. 

59.  GENERAL  EXERCISES 91 

60.  CONCLUSION Ill 

APPENDIX. 

TEN  FRAGMENTS  OF  VARIOUS  NATURES,  CAREFULLY  ANALYZED    AND 

DISCUSSED          .                    11. '5 


HARMONIC    ANALYSIS. 


PART    ONE. 

INTRODUCTORY. 

Section  1.  Definition.  Harmonic  Analysis  is  the  art  of 
accounting  for  the  various  chords  and  foreign  tones  which 
make  up  the  harmonic  structure. 

Section  2.  Requirements.  To  carry  on  the  study  of  Har- 
monic Analysis  successfully,  the  student  must  have  learned  enough 
harmony  to  be  able  to  write  exercises  employing  all  the  chords  of 
three  and  four  tones,  and  to  modulate  on  paper,  and,  if  possible,  at 
the  keyboard.  It  will  indeed  be  found  better  if  the  whole  course 
in  harmony  be  finished  before  taking  up  this  study.  In  this  event 
the  object  for  which  this  book  was  written  will  be  best  and  most 
easily  realized. 

Section  3.  On  Progressions  in  General.  Harmonic  Pro- 
gressions may  be  summed  up  briefly  as  follows  :  those  of  the  Fifth- 
Relationships,  up  or  down  —  V,  I;  I,  IV;  n,  vi,  etc.;  those  of  the 
Third-Relationships  up  or  down — V,  in;  I,  vi;  n,  IV,  etc.;  and  those 
of  the  Second-Relationships,  up  or  down  —  I,  II  ;  V,  vi ;  vi,  V,  etc. 

All  harmony  is  composed  of  the  elements  of  unrest  and  rest,  of 
the  progression  of  a  chord  more  or  less  dissonant  into  a  consonance, 
or  into  one  or  more  successive  dissonances  before  its  tinal  resolu- 
tion—  or,  the  reverse  of  this.  To  these  two  sound  phenomena 
are  attached  physical  and  psychical  impressions  which,  although 
they  exist  and  are  recognized,  seem  to  defv  a  final  analysis  and  to 
remain  beyond  satisfactory  examination  and  explanation.  These 
two  elements,  of  rest  and  of  unrest,  repeated  over  and  over,  with 
manifold  embellishment,  constitute  Music.  In  that  form  of  the 
Fifth-Relationship  in  which  the  root  falls,  is  found  the  most  natural 
resolution  or  progression  of  any  chord.  Thus,  the  ill  goes  to  the  vi, 

1 


2  HARMONIC  ANALYSIS. 

the  vi  to  the  II,  the  II  to  the  V,  the  V  to  the  I,  in  both  major  and 
minor,  and  the  nearer  the  progression  approaches  the  tonic  har- 
mony, the  more  gratifying  and  reposeful  the  effect.  Hence  the 
name,  Normal  Progression,  sometimes  applied  to  this  peculiar  suc- 
cession. To  modify  any  of  these  chord  successions  by  the  addition 
of  a  seventh  to  the  first  chord — as  Ir  IV,  or  HT  V  —  or  by  the 
chromatic  alteration  of  the  first  chord,  only  heightens  the  effect ; 
and  this  effect,  to  repeat,  is  the  impression  of  rest,  of  satisfaction, 
more  or  less  complete. 

All  other  progressions,  especially  if  they  employ  the  secondary 
triads,  have  in  them,  in  varying  degrees,  the  element  of  suspense,  of 
unrest ;  of  motion,  if  we  may  say  so.  Their  use  in  certain  schools  of 
composition  is  infrequent ;  in  other  schools,  especially  in  the  form 
of  the  Second-Relationships,  they  are  very  common.  Still,  startling 
and  interesting  as  may  be  many  of  these  progressions  above  men- 
tioned, the  student  will  find  that  the  I,  IV,  V,  and  n  in  the  Fifth 
and  in  the  Second-Relationships,  form  the  stock  in  trade  of  the 
composer  and  the  material  which  in  Analysis  he  will  have  most 
often  to  consider. 

Section  4.  Plan  of  Study.  In  pursuing  this  course  the  stu- 
dent is  expected  to  examine  carefully  the  examples  given,  with  due 
reference  to  the  text ;  and,  in  working  out  the  lessons,  to  indicate 
by  the  proper  signs  the  keys  as  they  occur,  and  the  nature — place 
in  the  scale,  and  inversion  —  of  each  and  every  chord ;  and  to  give 
to  each  foreign  tone  its  own  distinctive  mark.  Also,  where  required, 
lie  is  to  reduce  the  tone  structure  to  its  essentials,  one  of  the  most 
valuable  of  exercises,  directions  for  so  doing  being  given  at  the 
proper  place.  To  sum  up :  He  is  to  account  for  each  and 
every  tone,  whatever  its  duration  or  location.  All  lessons, 
unless  otherwise  specified,  may  be  marked  in  the  text-book  itself, 
the  signs  of  expression,  etc.,  having  been  omitted  to  make  sufficient 
room. 

Section  5.  Remarks  to  the  Teacher.  This  course  should 
be  taught  at  the  keyboard,  the  scholars  reading  the  figurings  in 
turn,  or,  in  a  doubtful  case,  the  opinion  of  the  whole  class  being 
found  before  a  decision  is  made.  Any  tendency  toward  super- 


HARMONIC  ANALYSIS.  3 

ficiality  which  this  method  would  seem  to  favor,  may  be  offset  by 
written  examinations  in  which  the  examined  must  know  —  or  fail ! 
The  class  should  enjoy  the  benefit  of  general  discussion,  and 
scholars  should  be  led  to  argue  for  their  figurings.  But  beware  of 
narrow  interpretations,  of  intolerant  views  ;  many  phrases  permit 
more  than  one  solution. 

The  teacher  is  recommended  to  teach  the  pupil  to  argue 
backward.  A  doubtful  passage  often  becomes  clear  if  one  looks 
on  and  finds  the  principal  point  toward  which  the  doubtful  passage 
tends. 

Furthermore,  to  each  section,  beginning  with  Section  14,  has 
been  added  a  set  of  References.  These  the  student  will  do  well  to 
look  up.  For,  unless  he  have  studied  Composition  and  thus  gone 
far  beyond  the  b.mnds  of  the  Harmony  Course,  it  cannot  be  possible 
to  make  him  ready  and  expert  by  the  use  of  this  book  alone;  and  so 
large  is  the  field  to  be  covered  that  a  fair  canvass  of  it,  such  as  has 
been  attempted  here,  tills  out  the  bounds  of  an  ordinary  sized  text- 
book. More  material  is  thus  necessary  —  us  any  one  versed  in 
teaching  can  see.  And,  lastly,  he  who  studies  by  himself,  by  look- 
ing up  these  references  and  marking  them,  can  give  himself  a  liberal 
education  in  Analysis  —  and  for  him  were  they  first  designed. 

AVe  have  drawn  from  the  following  material:  Beethoven,  the 
first  Piano  ti>n«(,<(x  ;  Schumann,  Album  for  the  YIHHKJ,  Op.  68; 
Bizet,  L'Arlefticunc,  Suites  1  and  II  :  Chopin,  /'/r/Vr/Vx — which  we 
would  advise  the  student  to  consult  constantly;  also,  C/erny, 
Op.  _!99  ;  Cramer,  Fifti/  Selected  tftmfiex  (von  Billow )  :  Chopin,  Xoe- 
ttt/'iiex  and  I'ulmniix,  ,s- ;  Schumann.  Dcti'itlsbihidlf)',  O\>.  ti.  and  /'<//;- 
fastest  He/.-e,  Op.  1  *J  ;  (Jrieg,  J'netie  Tune  I'ietnres,  ( )p.  .">.  1/it/HorfMjltes, 
Op.  ti,  LI/ rie  1'ieeex,  Op.  1  '2  ;  and,  lastly,  and  of  much  importance  to 
him  who  has  patience  to  examine  them,  Wagner's  Tunnhdiiscr  and 
The  F/f/i/if/  Dutflunun  (Xovello  Kdition). 

An  explanation  of  the  figures  used  in  making  these  References 
will  be  found  in  Section  1(1. 

Section  6.  Signs  Used  in  Marking.  A  capital  letter  shows 
a  major  kev  ;  a  small  letter  shows  a  minor  kev  ;  a  large  Roman 
numeral  a  major  triad  and  a  small  Roman  numeral  a  miner  triad; 


4  HARMONIC  ANALYSIS. 

the  sign  +  shows  the  augmentation,  and  the  sign  °  the  diminution, 
of  a  triad. 

Triads  in  major.  Triads  in  minor. 

I  I 

II  11° 

III  III+ 

IV  iv 

V  V 

vi  VI 


The  inversions  of  triads  and  of  seventh  chords,  both  principal 
and  secondary,  will  be  indicated  by  the  customary  figutiugs  : 
6,  *,  |,  *,  *,  attached  to  the  respective  Roman  numerals.  Or,  the 
letters,  a,  b,  c,  d,  meaning  root-form,  first,  second,  and  third  inver- 

7 

sioiis,  mav  be  used  with  these  same  numerals.     Thus  :  I  ,  I  ,  L,  11°, 

>.        »  aba 

77  +          * 

11°,  ii°'  IV  ,  in  ,  etc.     The  diminished  seventh  chord,  in  its  various 

?  b        °         -!i     !     °  °  ooo  f7o  7° 

forms,   will   be   marked  :    vn    ,  vii6,  viw,  vii4,  —  or  vn°    ,  vn°    , 

70  7,,  7o'  5'  3  2  a  b 

VII0      ,  VII0     . 
c  d 

Chromatic  alterations  will  be  discussed  in  their  proper  place. 
Section    7.     Principles    of   Analysis.    (Preliminary    State- 
ment.) 

No.  1.    Spell  each  chord  accurately. 

F-  has  one  significance,  F  another.     An  analysis  may  be  made 

incorrect  by  carelessly  calling  F5,  F.     Too  great  stress  cannot 

be  laid  on  this  point. 

Xo.  '2.    Build  up  the  chords  in  thirds. 

Seize  that  interval  most  apparent,  third  or  fifth,  and  build  from 

it  in  thirds  until  the  whole  chord  lie  found. 

Sections.    Triads  and  Seventh  Chords.    (Xo  Modulations.) 

"Write  the  numerals  and  the  signs  of  inversion. 

(It  has  been  found  impossible  to  divide  this  book  into  lessons, 

as  is  done  in  most  text-books,  and  the  plan  has  been  followed 

of  numbering  the  exercises  and  examples  straight  through.     The 

amount  of  work  to  be  assigned  to  a  pupil  is  thus  left  to  the 

decision  of  the  teacher.) 


HA  RMONI C  A  NA  L  YSIS. 


Exercise  1. 


Marked  Example. 
-•-     -•-     -»- 

—  ~ 


C  I      vi      IV    ni6    vi      n      V9     VVa       I6     V4     V6      I    IV     V7     I 

3  6 


2. 


_, m^ 


dZzziL— 


— rr — a  •  — i — 

gz  — * •        *        J— 

__, *_„  *    -  =±=t± 


l!^r^ 


=t=fr: 


^:-         ^t    ^_  i 

»=S~  Efizt^^^3B^S=  -B 

p 


— 9-     •  •  * 

* 


II A  KM  ONI  C  A  NA  L  YS1S. 


4. 


m|=£ — f- 

-E — r   i 


5. 


r 


*==* 

r — r 


*    £ 


-    -f 


V,       V7       V7 


7. 


f 


, |  _.  i_i ^r--+— -,—  fV 

fel- 


II A  AM/0A7  <     A  \A  L  ) 'SIS. 


8. 


- 

b:    •-  * 


|_Jid  tH7-!! 

2-    ~».  •-!   -—  * 


'•-_^  .0-  t    m     „        f 

— 5* — S^^*  M£     *'  f — ^"1  -  »  -  M    i         P*    • 

— . u »—  i_-i-«-     —i — « "-«     ^       •— r — b~r 

~0 P—  r-  *-|    *     •  — * 

_ 1 1 — , u-4— i— j , i_ — i— i .— 

^ 


Jj.'J—  ' ' 0—  — _ — 

-M=l — I— 1---\  4-^^f^ 


•- 


10. 

if 
"*^*»    ,1 

"4 


• 
•• 


*      *      » 

I      *     i       I     *    - 


KV^Z 

L-A 


* — »-r-* 


II 


ll. 


' 


rjj  ;: 


S-* 

i 


HA  RMONIC  A  NA  L  YSIS. 


Section  9.  The  Broken  Chord.  All  music  is  derived  from 
the  scale  and  the  chord,  the  latter  element  predominating.  The 
chord  ma)-  be  plain,  all  its  tones  sounding  simultaneously,  or 
broken  in  the  many  forms  of  the  arpeggio ;  that  is,  its  members 
may  be  sounded  one  after  the  other  in  a  great  variety  of  order. 
For  instance,  the  chord  structure  given  below  may  be  broken  in  the 
follDwino-  and  in  other  ways  without  making  a  change  of  chord. 


12. 


1 

q  .._ 

' 


:ir.g 


P| 

I 


*      * 


1 


F   1  \\- 


„ 1_ ..__»__;.  _fc_^-*= 


^^^ 


*-4-  F-f—      •"- 

t*"i      *i- 


a 


II A  RMON1 C  ANA  L  YSIS. 

Section  10.  Reduction.  It  will  be  observed  that  Examples 
«  and  /  show  a  compass  greater  than  that  of  the  primary  chord 
form ;  which  leads  to  the  General  Statement,  that  All  broken 
chords  may  be  reduced,  with  the  voices  which  accompany 
them,  if  there  be  such,  to  a  simple  four-part  structure.  In 
making  such  a  Reduction,  so-called,  the  extreme  notes  of  the 
florid  phrase  must  be  brought  into  proper  vocal  compass,  after 
which  the  inner  parts  may  be  added. 

Mark  each  chord  with  its  key  and  numeral,  and  in  the 
case  of  an  extended  broken  chord  indicate  by  small  notes 
the  Reduction  to  the  primary  chord  form. 


13.     Allegro. 


WACNKR,  Tannliausor. 


_  l££*££j* 

•      -^-    i=a^z-f.p^-»-r         =t±  *-=r^ 


BKKTIIOVKN,  i '].    10!i. 


^-\*  i 

•*i       *    • 


15.      Alley, 


S-^-w^i 


J5i:i  i  iiovrv,   <  )]i.  :>$. 


10 


II A  RMONI C   A  \A  L  YSIS. 


<         • 


16.     Presto  agitato. 


BEETHOVEN,  Op.  27. 


^ 

it        2  voices. 


Section  11.  The  Broken  Chord,  the  Appoggiatura,  the 
Passing  Tone,  and  the  Embellishment.  The  tones  of  a  broken 
chord  may  he  preceded,  all  or  some  ot!  them,  by  tones  foreign  to  the 


*  The  first  and  the  last  sopi-;iii<>  note  of  t;;u'h  two-measure  section  define  the  upper 
voice  in  this  case;   No.  17  is  different. 


77.4  RMO  XI C  A  XA  L  YSIS. 


11 


chord.  The  most  common  of  these  foreign  tones  are  those  men- 
tioned in  the  above  heading. 

The  Appoggiatura  is  a  foreign  tone  which  enters  by  a 
skip.  A  skip  is  any  interval  greater  than  a  major  second.  The 
Appoggiatura  may  enter  from  above  or  below,  and  must  move  a 
second,  major  or  minor,  up  or  down.  In  its  simplest  form  —  that 
here  given  —  it  moves  into  a  chord  tone,  and  may  have  any  time 
value,  long  or  short,  and  may  be  on  or  off  the  accent.  Other  varie- 
ties will  be  explained  later. 

SIGN  :  App. 


Model. 
18.     Virace. 


App. 


App. 


BEETHOVEX,  Variation. 
App.  App. 


Dominant  <  *ri:an-    \'7 
point. 

The  Passing  Tone  is  a  foreign  tone  which  stands  between 
two  chord  tones.  These  two  tones  mav  belong  to  one  ami  the 
jame,  or  to  two  different  chords,  and  the  Passing  Tone  may  be  dia- 
tonic or  chromatic,  accented  or  not.  The  interval  to  be  tilled  out 
may  be  a  second,  a  third,  or  even  a  fourth  ;  in  the  last  case  more 
than  one  diatonic  Passing  Tone  will  be  required.  Other  conditions 


12 


HA  RM  ONI  C  A  AM  L  YSIS. 


will  be  discussed  later.     The  examples  here  given  -will  show 
the  Passing  Tone  used  in  connection  with  one  chord  only. 
SIGNS  :  Accented  Passing  Tone,  O  ;  Unaccented  Passing  Tone, +. 


Model. 
19.     .1  llegretto. 


3.  CUTTER,  Verset. 
O     + 


F  I 


The  Embellishment  is  the  upper  or  lower  neighbor  of  a 
chord  tone,  and  proceeds  from  its  principal,  or  harmonic,  tone,  and 
returns  to  this  harmonic  tone.  The  Embellishment  may  move  a 
major  or  a  minor  second. 

SIGN  :  E. 


Model. 

20.     Con  moto. 
E 


B.  COTTER,  Etude. 

m 
E 


HA  RMONl  C  A\A  L  YSIS. 


13 


Mark  first  the  chords  in  an  example,  then  the  foreign 
tones. 


21.     Assai  lento. 

fSE^ESi 


CHOPIN,  Op.  28. 


22.     .- 


WAGKKR,  Taunhauser. 

JL 
-«--*- 

Ef"*^ 
_ 


— f — ^ — 


Reduce. 
23.     Ctintnhile. 


—*- 


1 


S<'jrr.MANN,  Op.  6. 


^^  g  f>>*    ' fgg-f ; . , ; 


14 


II A  RM  ONI  C  A  NA  L  YSIS. 


BKKTHOVEN,  Op.  35. 


One  chord  only  until  the  bar  line. 


Consider  each  eighth. 


Simili 


~ N- 


26.     Allegretto  vivace 


HARMONIC  ANAL YS/t. 


27.     Alleyro. 


IIcMMKi.,  Fantaisie. 

# 

.»-     + 


*"  Free  tone. 


4  flionls  in  this  measure.     3~ 


Section  12.  Modulation  is  a  change  of  key.  It  is  made 
ordinarily  by  a  dominant  harmony  with  its  resolution,  and,  ac- 
cording to  the  older  and  some  recent  text-books,  the  presence  of 
this  progression,  whenever  it  occurs  and  whatever  its  effect,  con- 
stitutes a  Modulation.  In  regard  to  this  matter,  however,  views 
have  become  modified  very  materially,  and  the  theorists,  as  in  many 
other  things,  would  seem  to  be,  on  the  whole,  behind  the  practicists, 
the  composers.  Indeed  there  is  ground  for  belief  that  from  the 
time  of  Haydn,  perhaps  from  that  of  Bach,  composers  have  thought 
it  possible  to  raise  and  to  lower  certain  scale  steps,  and  to  obtain 
thus  non-modulating  chromatic  harmonies,  which  sound  like  modu- 
lations but  do  not  leave  the  key. 

In  a  piece  in  C1  major,  for  instance,  we  may  tind  the  dominant 
or  diminished  seventh  of  D  minor,  with  its  resolution,  and  this  fol- 
lowed by  C  major  chords.  Some  theorists  contend  that  such  a 
progression  is  a  modulation  ;  that  any  chord  which  has  the  inter- 
vals of  a  dominant  seventh,  and  is  properly  resolved,  is  an  undoubted 
dominant.  Other  theorists  contend  that  a  real  modulation  is  made 


IK  HARMONIC  ANALYSIS. 

only  when  the  modulatory  process  is  confirmed  by  a  stay  in  its 
evident  key ;  that  these  seeming  modulations  are  only  intensifica- 
tions of  triads  of  the  key  other  than  the  primary  tonic,  generally 
the  subordinate  triads,  accomplished  by  the  use  of  their  seventh 
chords ;  and  that  these  chords  or  progressions  in  question  are  only 
altered  chords,  or  progressions  in  the  primary  key,  and  are 
to  be  so  marked.  They  quote  that  most  startling  and  familiar 
example —  the  end  of  t^tc  Lohengrin  Prelude,  by  Wagner  —  which, 
while  seemingly  moving  through,  or,  as  they  sometimes  say, 
"  touching  upon "  such  and  such  keys,  really  gives  the  ear  the 
impression  of  A  major,  wonderfully  enriched,  but  A  major,  all 
the  time ;  many  of  t-hem  conceding,  however,  that  this  is  an 
extreme  case.  A  third  party  of  theorists,  acknowledging  the  diffi- 
culties of  the  matter,  holds  that  while  this  passage  in  question  may 
be  in  A  major,  to  mark  .the  many  chromatic  harmonies,  as  chro- 
matic alterations  in  this  key,  is  to  strain  the  key  unwarrantably  ; 
they  would  call  each  apparent  change  of  key  a  real  change,  with 
a  mental  reservation  as  to  the  correctness  of  the  analysis  ;  would, 
perhaps,  write  two  figuring*,  each  one  tenable,  and  depending  on 
the  point  of  view. 

In^opposition  to  all  this,  the  old-school  men  say  that  the  modern 
ear  has  heard  so  many  modulations  that  it  has  become  blunted, 
dazed  ;  that  if  the  ear  were  fresher  and  keener,  it  would  call  each 
progression  in  question  an  undoubted  change  of  tonality ;  and  they 
refer  their  opponents  back  to  the  impressions  of  youth,  when  each 
chord  change  ravished  the  auditory  nerve,  and  each  seeming  shift 
in  the  seat  of  key,  however  fleeting,  was  felt  as  a  genuine  thing. 
They  say.  further,  that  the  short  and  fleeting  modulation,  the 
Digression,  so-called,  is  as  much  a  part  of  the  composer's  stock  in 
trade  as  that  deliberate  modulatory  procedure  in  which  the  forces 
of  the  key  are  drawn  up  in  array. 

In  this  matter  it  is  difficult  to  lay  down  a  hard  and  fast  rule. 
In  many  instances  the  analyst  must  use  his  own  judgment,  and 
the  ear,  which  is  plainly  the  last  court  of  appeal,  must  be  called 
upon  to  decide.  And  as  cars  do  not  always  hear  alike,  the  validity 
uf  more  than  one  interpretation,  based  on  the  individual  point  of 


HARMONIC  ANALYSIS.  17 

view,  is  evident.     We  would,  however,  add,  that  while  the  theory  of 
altered  chords  may  often  be  the  theory  most  plausible,  cases  will 
occur  in  which  the  only  satisfactory  explanation  is  that  of  a  sudden 
and  passing  but  unmistakable  change  of  key. 
Section  13.     Principles  of  Analysis. 

1.  Spell  each  chord  accurately. 

F*  has  one  harmonic  significance,  F  another.  And  an  analysis 
may  be  made  incorrect  by  carelessly  calling  F*,  F. 

2.  Build  up  chords  in  thirds. 

Seize  that  interval  most  apparent,  third  or  fifth,  and  build  from 
it  in  thirds  until  the  whole  chord  be  found. 

3.  The  identity  of  a  chord  depends  on  its  resolution. 

In  other  words:  judge  a  chord  by  what  it  does!  Always  look 
ahead.  Any  chord  may  be  taken  as  a  harmony  in  one  key 
and  quitted  as  a  harmony  in  another  key  ;  or  it  may  belong  to 
one  key  alone  ;  or  it  may  be  an  altered  chord ;  it  is  well  to 
remember  these  three  possibilities. 

4.  Reduce    harmonies  to  principal  chords,   if  possible. 
The  in  and  the  vi  usually  occur  in  sequences.     The  I,  V,  IV,  and 
n,  with  their  various  derivatives,  will  generally  be  found  surti- 
cient  for  both  classical  and  modern  music.     Hence,  in  analyz- 
ing, first  get   out  the    chord   structure,    makiiuj    it    as  simjilc  as 
possible,  and  then  f/o  buck  and  murk  the  foreiyn  tones. 

o.    Place  as  many  chords  as  possible  in  one  key. 

6.  A  major  triad  used  as  an  opening  chord  should  be 
regarded  as  a  tonic  harmony. 

Instances  to  the  contrary  are  rare,  although  they  do  occur. 

7.  The  normal  chord  change  falls  on  the  accent. 

The  use  of  this  principle  will  simplify  many  places  otherwise 
complicated  and  difficult.  If,  for  instance,  the  Y  lie  before  the 
bar-line  or  before  the  third  beat  of  a  measure  in  four-four  time, 
and  only  one  member  of  the  chord  of  resolution  be  on  the  fol- 
lowing accent,  this  one  tone,  especially  if  it  be  the  bass  tone, 
defines  the  chord  and  causes  the  other  tones  to  be  unessen- 
tial, suspensions,  appoggiaturas,  etc.. -— provided  that  the 
other  members  of  the  rightful  chord  of  resolution  enter  later 
in  the  measure. 

8.  A  six-four  on  the  accent  may  be  regarded,  in  nearly 
every  case,  as  a  tonic  harmony. 


18  HARMONIC  ANALYSIS. 

9.  Any  scale  step  may  be  changed  chromatically  with- 
out causing  a  desertion  of  the  key,  if  the  chromatic  chord 
be  followed  by  a  principal  chord  of  the  reigning  key. 

The  "  identity  of  a  chord,"  then,  "  depends  oil  its  resolution." 

10.  Modulation.     Made  (1)  by   the  V,    in    its   various 
forms ;  (2)  by  a  *  on  the  accent,  the  root  becoming  a  tonic  and 
drawing  after  it  a  cadence,  —  a  progression  which  may  also  follow  ail 
unaccented  *,  although  infrequently  ;  (3)  by  the  II  in  its  various 
forms,  this  chord,  often  called  a  "  chord  of  approach,"  moving  into 
a  cadence  through  its  tendency  toward  the  dominant ;  (4)  by  any 
of  the  triads  of  a  key,  even  the  weakest,  the  in,  in  which  especial 
case  the  establishment  of   the   key   may  require  several   charac- 
teristic chords,  most  often  the  succession,  in,  vi,  n,  V,  I,  altered 
or   diatonic,  with   or   without   sevenths,  inverted  or   not;  (5)  by 
taking  a  tonic,  and  afterwards  establishing  it,  the  so-called 
Assumption  of  a  Key ;  (6)  by  enharmonic  means  ;  and  (7)  by 
a  change  of  mode,  the  change  being  usually  made  from  a  tonic 
harmony. 

11.  An  apparent  dominant  seventh  must  be  tested  as 
to  its  resolution  and  its  surroundings. 

A  chromatic  chord,  apparently  a  dominant  seventh  —  having 
all  its  intervals  —  will  often  appear  and  disturb  the  analysis. 
Unless  it  fixes  the  key  strongly  on  the  mind  through  legiti- 
mate resolution  and  sufficient  duration,  it  may  best  be  regarded 
as  an  altered  chord,  in  most  cases  as  a  supertonic  seventh, 
chromatically  changed.  Principle  Number  3  must  be  borne  in 
mind.  If  an  apparent  V  of  G  major  stands  between  two 
strong  C  major  chords,  it  is  an  altered  chord  in  C  major,  and 
nothing  else. 

12.  Modulations  should  be  marked  as  belonging  to  the 
next  related  keys  ;  i.  r.,  from  C  one  goes  to  G,  e,  a,  F,  d. 

If,  for  example,  in  C  major  the  1)  major  tonic  appears  after  its 
dominant,  the  dominant  must  be  marked  as  1)  minor  and  the 
major  tonic  as  I)  major,  involving  a  change  of  mode. 

13.  "When  a  seventh  chord  does  not  contain  the  elements 
of  a  V    — major   third,   perfect   fifth,  minor  seventh  —  nor  of  a 
VII      —minor  third,  diminished   fifth,  diminished  seventh — this 
chord  may  be    regarded    as  a  supertonic  seventh. 


HARMONIC  ANALYSIS.  19 

In  the  great  majority  of  cases  this  interpretation  will  be  found 
to  be  correct,  for  the  seventh  chords  on  the  other  steps  of 
the  scale,  are  rarely  used  save  in  sequence  progressions. 

14.  "When  in  a  rapid  tempo  a  chord  is  repeated  with 
more  than  one  bass  note,  that  is,  with  change  of  inversion, 
the  first  appearance  of  the  chord  is  usually  the  one  to  be 
figured. 

15.  Any  member  of  a  chord  may  be  omitted  without 
causing    the    chord    to    lose   its    identity ;    an    incomplete 
principal  harmony  must  not   be  regarded,  however,   as  a 
secondary  chord. 

16.  Chromatic  alterations  may  be    indicated,  if  neces- 
sary,   by   placing   in    brackets    below   the    Roman   chord- 
numerals,  the  figures  for  the  chord   accompanied   by  the 
proper  accidentals. 

n 

Thus,     s     signifies  that  the  supertonic  seventh  is  in  its  first 
LjaJ         inversion  with  raised  root  and  third. 

17.  The  nature  of  a  major  triad —  whether  dominant  or 
tonic  —  when  standing  at  the  end  of  a  phrase,  may  often  be 
best  decided  by  ear. 

The  effect  of  a  Tonic  is  that  of  rest,  of  finality  ;  the  efi'eot  of 
a  Dominant  is  that  of  suspense,  of  something  to  come. 

18.  The  chromatic  chord  which  precedes  a  modulating 
dominant  seventh  or  tonic  six-four  chord  —  usually  a  dimin- 
ished seventh  or  an  augmented  chord  —  is  to  be  placed  in  the 
key  of  this  modulating  seventh  or  tonic  six-four  chord. 

This  is  the  natural  outcome  of  Principles  Numbers  3  and  5. 

Section  14.    Real   Modulations. 

Shown  by  an  extended  and  deliberate  progression  in  the  new 
key,  or  by  rapidly  shifting  key  clusters.  Mark  as  before. 
Xo  further  directions  would  seem  to  be  needful  as  to  this 
point. 


20  HARMONIC  ANALYSIS. 

28.     Moderato.  MOZAKT,  March. 


9  -*—  ~?~~ 


--*-« 


J- 
I 


j , — - — I j '-4—- 1 


* 


29.     Allegro  risoluto. 


BEETHOVEN,  Marc-h. 


— I — 


_l — 1 1 . , — . 1 -\ — ^ — 


^--g^EgE^ 


;>«*    "  — •— 

i±t=*-   -• — *  — «— i— 1|-  ^~*  --»    I    »    •  ~-d  -rH 

* 


HA  KM  ONI  C  ANAL  YSIS. 


21 


DIAHKI.M,  Waltz. 
V 


E£ 


: 


Ej^E  g^^^g^^-i^r^rtg^ 

_,_   ^i^S        „          *-   *      -.-    -    ^  ^ 


!    1^ 
«       —       ^ 


II 


PART   TWO. 

THE    NON-HARMONIC    TONES,   IN    DETAIL. 

Section  15.    References. 

Explanation  of  Signs.     The  Roman  numeral  stands  for  the 

movement ;  the   Arabic  numeral  immediately  following  stands 

for  the  measure.     In   counting  the  measures,  Measure  1   is  the 

first  full  measure,  the  tirst  measure  beginning  with   a    down 

beat ;  in   other   words,  any  fractional   part   of  a   measure  with 

which  a  piece  may  begin,  does  not  count.     More  than  this  — 

repeat  signs  have  no  value. 

Thus,  Beethoven,  Op.  10,  No.  2,  I,  19,  means:  Beetluven,  opus 

ten,  second  sonata,  first  movement,  nineteenth  measure. 

In  some  cases,  where  the  movement  is  short,  no  measure-figures 

have  been  given. 

Section  16.     The  Appoggiatura  (continued}. 

This  ornament  may  move  not  only  into  a  chord  tone,  but  into 

some  other  non-harmonic*  tone  also. 

Both  neighbors  of  a  chord  tone  may  also  be  taken  immediately 

before  the  chord  tone  itself,  forming  a  Double  Appoggiatura,  and 

occasionally    one    of    these    tones    is    repeated,    forming    a    Triple 

Appoggiatura. 

We  have  also  applied   the  term  Appoggiatura  to  that  foreign 

tone  which  enters  something  like  an   Embellishment,  but  after  a 

rest  ;  and   also,  to   that   foreign    tone   in  a  scale  passage  which   is 

taken  by  a  step  or  skip  of  an  augmented  second. 

SK;NS:  Appoggiatura,   A  pp. ;    Double^  Appoggiatura,    D.    App.  ,- 

'vriple  Appoggiatura,  T.  App. 


24 


HA  R  M  ONI  C  A  XA  L  YSIS. 


31.     Lento.  SCIIUUKUT,  Song. 

""" 


rr^r^i^r 


J] 


32.     Co?i  molto  agitazione. 


WEBER,  Concertstiick 


33.     Allegro. 


CHOPIN,  Etude. 


*£-=* 


i 


e   I 


34.      Molto  lento.  SCIU'MANN,  Op.   68. 


I     , 

E^I  i  E; 


»    ^    _  _a: 


rs: 


HA  UM  <>M  < '   A  AM  L  YSIS. 


25 


35.      A  llegretto. 


\\.  CITITKK,  Etude. 


\ 


H  _!*j_  J3L __*& .i_J3i « *  >  =?• 

^IT  --JT^gE^E^E^T"  :Ej5==y";- 

L/  "p  ^  v 

.  r  j  ' 


fe"'  ' 


II 


36.      J're.t.'u  cnii  Juuco 


N,  Prelude. 


KKKKHKNCKS.     Appogg    :   Beethoven,  ( )j>.  7,  IV.  :>4  ;  Op.    10.  No.  1,  III, 

4:!;  Op.  10,  No.  2,  1.19:  Op.  lo.  I,  .-1//0.,  25;  C/t-rny,  Op.  L'9!i.  No.  ol.  second 

i  part;   Cramer,  Ktude  G:    Hi/.ct,    I/Arlc'sicnne.  Suite   No.  1.  Un  poco  jii'u  Imto. 

Double  Appogg.  :   lieethoven.  Op.  7.  IV,  -Is  ;   Op.  2,  No.  1,  L'tJ ;   Cliopin,  1're- 

lude  No.  l:J:  C'/crny.  Op.  2!»9,  N...  11  ;  Cramer.  Etude  K>,  Ktude  28. 


Section  17.  The  Appoggiatura  Chord  is  a  chord,  usu- 
ally chromatic,  which  has  as  its  soprano  tone  a  genuine 
Appoggiatura.  Tin-  inner  voices  which  accompany  the  soprano 
tone  may  be  passing  tones,  suspensions,  any  kind  of  foreign  tones. 
Such  a  chord  precedes  a  principal  harmony,  and  if  its  tones  be 
stricken  out,  omitted,  this  principal  chord  will  appear  as  one  of  the 
harmonic  essentials.  The  AppoggiaUira  Chord  generally  appears  on 
the  accent. 

SIGN-.  App.  <'M 


26 


HA  KMOyi  C  A  XA  L  i 'SIS. 


37-  Auagio. 


BIZKT,  L'Arlesieniie. 


F    =&= 

fc£E  ^^j^§ 


r>.     rt  -»' 

-*-* — HI — 


RKKKKKNCKS.  Beethoven,  Op.  2,  No.  ;5.  IV;  Op.  7,  II,  8;  Op.  10, 
No.  2,  If,  IP  strain;  Cramer,  Etude  4,  m.  19;  Etude  19,  m.  18;  Et.  14,  m.  6; 
Schumann,  Op.  6,  No.  9,  in.  1;  Bizet,  L'Arle'itienne,  Suite  No.  1,  I,  I'n 
piiilento.  in.  !S  :  Wagner,  '/'(tiini.tiiixcr,  2-59,  in.  1. 


Section  18.  The  Free  Tone  is  a  foreign  tone  whicb 
is  quitted  by  a  skip,  up  or  down,  and  is  not  a  member 
of  the  following  chord.  It  may  be  used  after  a  foreign  tone 
of  any  kind.  It  is  rare  in  the  classics,  but  frequent  in  certain 
modern  works. 

Sinx  :   F.  T. 


CilM  E<i.    '  '{).     tj 


II 


HA  KM  ON  1C  ANALYSIS.  21 

B.  CUTTER,  Etude. 


• f~~  -n 

E  ^  =1 


REFERENCES.  Wagner,  Lohengrin,  p.  10  ;  Bizet  //  Ir.esienne,  Suite  1, 
II,  m.  52,  etc.;  (irieg.  Op.  (i,  Xo.  1,  in.  22. 

Section  19.    The  Passing  Tone  (continued). 

The  Passing  Tone  may  be  used  when  two  members  of  a  chord 
remain  stationary. 

Also,  two  or  three  voices,  in  the  latter  case  funning  chords,  may 
move  from  a  principal  chord  to  another  principal  chord  some  dis- 
tance, away  ;  those,  chords  which  are  passed  through  have  no  har- 
monic significance,  and  only  the  end  chords  need  to  be  marked. 

Lastly,  Passing  Tones  may  be  broken,  if  the  tempo  be  rapid,  in 
the  form  of  thirds  or  sixths,  or  even  in  octaves  ;  sec  Appendix,  Kx.  h". 

40       Antlantino.  Scm  MAN- 


u 


28  II A  KM  OX  1C   AX  A  LYSIS. 

41.     Presto.  BEETHOVEN,  Variation. 


>! 


f^^i 


1*1  1 


==1 
: 


42-     Andaniino  grazioso. 


CZEHNY,  Op.  365. 


RKFKREXCKS.     Wagner,  Tannh^iimer,  p.  5  :  Fh/ing  Dutchman,  p.  135,  in.  12. 


Section  20.     The  Embellishment  (<-oiitinued). 

The  Embellishment  may  ornament  a  foreign  tone  as  well  as  a 
chord  tone.  Also,  in  carrying  out  a  figure,  a  chord  tone  may  be 
used  to  embellish  a  passing  tone.  Furthermore,  two  voices  may 
be  embellished  simultaneously,  and  these  voices  may  be  broken  as 
are  the  Passing  Tones  in  Section  19,  No.  42. 


43.     Allegro  molto 

1 


IIAJlMOiMC  ANALYSIS.  29 

BEETHOVEN,  Quartet,  Op.  59,  No.  3. 


1  \>l  i      =£=' — =1=  — J=±=t=i  = 


RKFERKXCKS.     Beethoven,  Op.  2,  No.  1,  IT,  17;  Czerny,  Of.  299,  No.  4, 
m.  14;   Schumann,  Op.  6,  No.  7  ;   Chopin,  Nocturne  G,  in.  8. 


Section  21.  The  Embellishing  Chord  is  a  combination 
of  tones  accompanying  an  Embellishment  in  the  soprano, 
and  may  form  a  definite  chord,  built  up  in  thirds,  or  no 
chord  at  all.  It  may  be  diatonic  or  chromatic.  Omit  it  and  the 
essential  chord  will  appear,  visible  to  the  eye. 

More  than  this,  composers  very  frequently  use  as  Embellishing 
Chords,  altered  diminished  seventh  chords  based  on  different  steps 
of  the  scale.  Most  common  are  those  on  the  sharp  second  and 
sharp  sirth  steps  of  the  major  mode.  Thus  :  0  major,  d5,  i*,  a,  c  ; 
a*  c$,  e,  g.  Of  these  the  altered  supertonic  seventh  embellishes  the 
tonic  harmony,  and  the  altered  submediant  the  dominant  harmony. 
Occasionally  an  enharmonic  notation  (see  Section  34)  of  one  of 
these  two  chords  will  occur;  in  C  major  d^  being  made  e17,  etc. 
These  changes  result  from  careless  s] telling,  or  from  some  need  of 
voice  writing.  Furthermore,  either  one  of  these  two  chords  may 
appear  without  its  third  or  fifth. 

SIGNS:  E.  Chd.,  or  E.  Olid, 
it 


II A  KM  0X1 C   A  XA  L  YS  /.S. 
44.     Allegro  vico.  BIZKT,  Carmen. 


45.     J  llngretto. 


LISZT,  Les  Preludes. 


^p^     E!?  ^^f^?! 


^±2 


KKFK.KKNCKS.      ISfetlioven.  ()j>.  J.  Xo.  :5.  Ill;  Cramer,  Ktndc  1-1,  in.    1,2, 
etf.  :   Bi/et.  L'Arlt  'xienne.  Suite  Xo.  1,  I.  fifth  last  measure:   ih'ul.  II,  in.  18. 


1IA11MO\H'    . I. V.I M>7> 


31 


Section  22.  The  Suspension  is  the  delayed  or  retarded 
entrance  of  a  chord  tone,  or  of  a  foreign  tone,  and  is  possible 
only  when  a  voice  moves  down  a  major  or  a  minor  second. 
Suspensions  mav  occur  singly  or  in  pairs ;  three  voices  may  even 
he  suspended  at  one  lime,  or  the  whole  chord  be  suspended  rhyth- 
mically. The  Suspension  mav  be  plain  or  ornamented.  Double 
suspensions  will  often  produce  combinations  which  may  lie  regarded 
as  subordinate  seventh  chords ;  in  analyzing  it  is  well,  however, 
to  regard  such  combinations,  when  possible,  as  Suspensions,  pure 
and  simple,  and  to  thus  carry  out  one  of  the  first  Principles  of 
Analysis  —  that  of  making  as  few  chords  as  possible,  and  these 
firui-ip  'I  chords. 

The  res  ilution  of  the  single  Suspension,  and  occasionally  of  the 
double  Suspension,  though  rarely,  may  be  made  into  some  chord 
other  than  the  chord  to  which  the  tone  of  resolution  in  the  rirst 
place  belonged. 

The   resolution  of    the    Suspension    may    be   ornamented    in   a 
number  of  ways. 
SK;N  :  S. 


47. 


MO/ART,   Variation. 


SoiHMANN,    (>J>.    t>S. 


II 


HARMONIC  ANALYSIS. 


49.     Mlftjreito. 


Sciirm:RT,  Impromptu. 


50.     Allegro.  BEETHOVEN,  Op.  14. 


RKFKKKNCES.  Beothovcn,  Op.  7,  II,  6:  Op.  2.  Xo.  1.  I,  11  :  Cramer, 
Etude  25.  rn.  2  :  Schumann,  Op.  12,  Xo.  1,  m.  2  and  21  :  Chopin.  Prelude  No.  2. 
ra.  11,  12:  Prelude  Xo.  4  (essential  chord  at  end  of  each  measure):  Bizet, 
L' .\  rlc'sienne,  Suite  I.  Andantinn,  rn.  2,  3;  Wagner,  Flying  Dutchman,  p.  4  (thr°« 
chords  in  two  Tiiea«ur*"<). 


HA  RMONIC  ANA  L YS/S. 


33 


Section  23.  The  Anticipation  is  the  premature  entrance 
of  a  tone,  essential  or  foreign,  and  is  the  opposite  of  the 
Suspension.  The  German  term,  Vorausnahme,  roughly  trans- 
lated as  the  tliing-taken-be forehand,  explains  this  phenomenon 
finely.  Principle  No.  4  should  be  borne  in  mind.  The  Anticipa- 
tion may  include  a  whole  chord,  with  a  skip  in  bass.  Rather 
infrequent  in  occurrence. 

SIGN:  A. 


52.     Lento. 


£+- 


BACH. 


53.     -I // 


B.  (.'UTTKK,  Sonata. 


' 


^      «* 


Pl-5 


ll 


RKFKKKMKS.    Chopin,  Prelude  No.  !>,  in.'J  ;  Wagner,  Fl>jin<j  Dutchman.  L'.''!. 


34  tiAHMOXIC  ANALYSIS. 

Section  24.  The  Free  Anticipation  is  a  foreign  tone, 
quitted  by  skip,  which  belongs  to  the  following  chord.  In 
this  respect  it  differs  from  the  Free  Tone. 

SHJX:  F.  A. 


54.     Velnce. 

-»-  -*- 


B.  CUTTER,  Etade. 


55.     Andante.       BRAHMS,  Sym.  No.  4. 


•-z^f-ES — 0 —          —  * — « 

— .   -- — LJt 1 1 1 — *J  - 

5  * 

REFERENCES.     Beethoven,  Op.  13,  III,  1;  Oieg,  Op.  12,  No.  5. 

Section  25.  The  Retardation  is  a  rising  Suspension, 
and  is  generally  accompanied  by  one  or  more  Suspensions.  A 
whole  chord  may  also  he  retarded,  one  single  chord  tone,  or  even 
.A  foreign,  tone,  or  tones. 

SIGN:  K. 


56.     Andantino. 


B.  CUTTER,  Canzona. 


HARMONIC  ANALYSIS.  35 

57.     Molto  Allegro.  B.  CUTTER,  Etude. 


REFERENCES.     Beethoven,   Op.   10,   No;   2,11,10;  Op.  2,  No.  2,  I,  60; 
Bixet.  L'Arlesienne,  Suite  No-  1,  I,  £7n  porn  piii  lento,  m.  8,  etc. 


Section  26.  The  Organ  Point ;  the  Pedal.  The  Organ 
Point  is  a  held  tone,  over,  or  under,  or  around  which  move 
harmonies  containing  more  or  less  frequently  this  held  tone 
as  a  member.  The  Organ  Point  may  be  short  —  three  chords  in 
length  —  or  it  may  be  given  great  extension  ;  the  held  tone  may  be 
the  tonic,  the  dominant,  or  botli  together,  the  subdominant,  or  the 
mediant ;  and,  lastly,  and  of  frequent  occurrence,  the  Organ  Point 
may  be  broken  or  interrupted  by  rests,  or  may  be  ornamented  by 
some  foreign  tone  or  tones. 

The  harmonic  structure,  whether  above  or  below,  is  to  be  regarded 
as  a  thing  by  itself,  and  figured  as  such  ;  if  above,  the  actual  bass 
is  the  voice  immediately  over  the  held  tone,  and  the  figuring  should 
begin  from  this  voice.  One  reason,  and  perhaps  the  best,  for  this 
procedure  is  as  follows :  if  an  organ  point  in  C  major,  and  on  (\  con- 

a     d 

tains  the  succession   /"  6,  and  the  figuring  be  made  to  include  the 

/)  G 
held  tone,   tben   the   first    of  these    two  chords   must   be  a   super- 

6 

tonic  4  ;  which,  as  the  seventh  in  the  bass  does  not  come  to  a  reso- 

2 

lution,  is  absurd  ;   (',  then,  has  nothing  to  do  with  the  chord. 

SKINS:  Tonic  Organ  Point,  T.  O.  P. ;  Dominant  Organ  Point, 
D.  O.  P. ;  Mediant  Organ  Point,  M.  0.  P. ;  Double  Organ  Point, 
Dbl.  0.  P. 


36  HARMONIC  ANALYSIS. 

58.     Andnntinn.  SCHUMANN,  Op.  68. 


-&-£-£— 

zt^zffcr: 

fcaz: 


=CT 


3     •*- 


G   T.  O.  P. 
Ibid. 


,  .x5_.          ^_.         .^  .         .^,_.  ^  -,5..          ^  ^  . 

& 


59. 


BEETHOVKN,  <  >p.   10,  No.  3. 


=F-       • 

-  ^  •       _  __ — .  _• 


HMIMOMC  AXALYX/S. 


37 


- 1  lltyrii  aaxui. 


HIZKT,  L'Arle'aienne. 


RKKKKKXCKS.  Beethoven,  Op.  2,  No.  3,  III,  29;  Op.  10,  No.  :-J,  I,  93; 
Schumann,  Op.  12,  No.  8,  in.  45;  Grieg,  Op.  G,  Nos.  1  and  4;  Op.  1!»,  No.  2  ; 
Chopin,  Prelude,  No.  8,  and  Nocturne,  No.  2,  in.  1;  Hi/et,  //Arlc'sienne, 
Suite  1,  Le  Carillon:  \Vagner,  Flying  Dut  Imtun,  12.~>. 

Section  27.  Dispersion  of  Chord  Members.  The  normal 
chord  change  is  a  simultaneous  one.  The  members  of  a  chord  may, 
however,  enter  at  different  points  of  the  measure,  and  the  harmony 
must  be  determined  by  picking  out  the  various  chord  tones.  Prin- 
ciple No.  4  must  be  borne  in  mind.  Such  irregular  entrances  are 
made  only  on  principal  chords ;  for  a  subordinate  chord,  used  in 
such  a  manner,  would  weaken,  perhaps  destroy,  the  key  character  — 
which  is  absurd.  These  irregular  entrances  may  be  caused  by  any 
of  the  foreign  tones. 


62.     Con  uniina. 


SCIH'MANX,    Op.    68. 


I] 
SHSiz    fl 


HKKKKKNCKS.      Sciiir.nann.  ()p    ;'S.  No.  2".  in.  i'^!;   Cliopiu,  Preluded. 


//.  1  RMO.\I  C  A  NA  L  V.S/.S. 


Section  28.  Tones  sustained  by  Damper  Pedal  of  the 
Piano.  Mistakes  are  often  made  in  the  analysis  of  piano  music  by 
overlooking  the  continuance  of  a  tone  by  the  damper  pedal  after 
the  key  struck  has  been  quitted  by  the  ringer.  Neglect  of  this 
point  will  often  render  an  analysis  quite  incorrect.  In  music  care- 
lessly marked  as  to  the  pedal  signs  —  in  Schumann,  for  example  — 
some  discretion  is  called  for  ;  it  may,  indeed,  become  necessary  to 
supply  missing  signs.  Use  the  principal  chords. 


64.     Lento,  con  tenerezza. 


SCHUMANN,  Op.  68. 

»—  •— «- 

J-i 


—3  *-f~*  v          :_ntl3E_l f^^L1 

"'  ^r       ?t** 


-^-4—^  

^ 

PART    THREE. 

MODULATION    IX    GEXEKAL,   THE    ALTERED 
CHORDS,   ETC. 

Section  29.  Altered  Chords,  which  have  already  been 
touched  upon,  may  be  known  by  their  resolutions.  An 
Altered  Chord  moves  to  a  principal  chord  of  the  key  in 
which  it,  the  altered  chord,  is  chromatic. 

Any  step  of  a  scale,  major  or  minor,  may  be  changed  chromati- 
cally, some  of  the  changes  being  the  result  of  passing  tones,  others 
being  chord  changes  made  to  heighten  the  effect  of  the  chord  itself. 
Thus,  in  the  latter  case,  the  natural  tendency  of  the  supertonic 
seventh  chord  toward  -the  dominant,  or  toward  its  chord  of  intro- 
duction, the  tonic  sixrfour,  is  increased  in  the  major  mode,  if  by 
lowering  the  iifth  of  the  supertonie  chord  this  supertonic  be  made 
somewhat  more  dissonant. 

It  must  ever  be  borne  in  mind  that  many  chords  are  defin- 
able as  Altered  Chords  only  through  their  surroundings. 

What,  for  example,  might  cause  the  mental  effect  of  a  modula- 
tion in  a  slow  tempo,  must  be  regarded  as  a  chromatic  alteration  in 
a  rapid  movement. 

Section  30.     The  Supertonic  Seventh  with  Sharp  Third. 


HKKTHOVKN,  ( >j>.   14. 


40  HARMONIC  ANALYSIS. 

66      .1  ndanle  con  moto. 


MENDELSSOHN,  Song  without  Words. 
simili 


11 


r*^z^x^\'~^~         -•—    — aa— 
'— *~^-Z-t— \— ^_    \^\ L: — i 


-& — •&- 


UKKKKKNCES.  Beethoven,  Op.  7,  II,  19,123:  Op.  10.  No-  2,  I,  57;  Op.  10, 
No.  3,  II,  5  ;  Chopin,  Prelude  13,  piu  lento,  m.  7;  Schumann,  Op.  12,  No.  3, 
m.  1. 

Section  31.  Other  Altered  Steps.  Made  so  by  their  sur- 
roundings. 


67.     Allegro. 
$      =1 


MOZART,  Sonata. 


— 

- j  — 

C*a 


^t'_ 


m 


\ 


H  A  RM  ONI  (     A  A  /I  L  YS/S. 


68.     Molto  cantabile. 


SCHUMANN,  Op.  68. 

n 


69.     Andante. 


BRAHMS,  Op.  45. 


| 


RKKKUENTKS.  Beethoven,  Op.  10,  \o.  1,  TIT,  37;  (irieg,  Op.  6,  Xo.  4, 
in.3;  C/cniy,  Op.  2!»£),  No.  L>7  ;  Cramer,  Ivmle  !»,  in.  50;  Etude  111,  in.  7; 
Chopin,  Nocturne  No.  2,  in.  11;  No.  fi,  in.  M;  Scliuiuann,  Op.  t!8.  No.  17, 
in.  13  and  17;  No.  'J(5.  in.  3:  No  'JS,  in.  3,  7,  'JO:  No  30.  in.  L'.  3,  7;  No.  38, 
m.  3;  No.  39,  in.  'J7:  Hi/et,  L'Arl('siennr.  Suite  I.  First  Movement,  Tempo  I; 
Wagner,  Tnnnln'intir,  I'll.  'Jl'O.  L'^JS.  '_'.">•};  f-'/i/int/  Dutcinnan.  13. 

Section  32.  Apparent  and  Real  Modulations.  These 
Apparent  Modulations  may  often  be  regarded  as  intensifi- 
cations of  secondary  scale  steps,  through  the  precedent  use 
of  their  apparent  dominant  or  diminished  seventh  chords  - 
as  has  already  ItotMi  stated  :  or.  as  a  series  of  dominant  seventh 
chords  preceding  a  cadence,  the  roots  involved  U'ino-  usually 
the  ill.  VI.  n.  V.  I  (see  Appendix.  No.  1  ). 


42  HARMONIC  ANALYSIS. 

Whether  or  not  real  modulations  are  present,  each  analyst  must 
decide  for  himself.  At  all  events,  the  succession  in,  vr,  n,  V,  with 
or  without  sevenths,  and  in  whatever  form,  is  one  which  confirms 
the  ultimate  tonic;  it  is  one  in  which,  however  strong  these  ques- 
tionable key  impressions  may  be,  the  total  impression  is  one  of 
pushing  on  to  the  close  in  that  iinal  tonic  harmony  which  rounds 
out  the  whole.  This  feature  of  the  thing  leads  many  to  say  "  al- 
tered chords  "  where  the  man  of  the  old  school  savs  "  modulation." 


71.     A  ndante. 


SCHUBKKT,  Violin  Sonata. 


:2^=J=    =j 

A 

ZM       * I 


J  J 1 — ^-haj-r •*-*—-      r+S*-9-*-^'^    ' 


72.     Allegro  deciso. 


SCHUMANN,  Op.  15. 


t       *—~~i 


HARMONIC  ANALYSIS.  & 

73.    Andante  maestoso.  WAGNER,  Tannhauser. 


Z%3^=£ 


T 
' 


i        i 

74.     Tempo  di  marcia. 


r, _ 
^>: 


BIZET,  L'Arlesienne. 

^^L-=J- 


— X- 


-*-^ 


J 


_>>_-  0—i  —g— 

^P- 


± —  — * _|_cf±jrz^Zl  —  *^ 

^Fr^=^" 


^=h-t:    E-"1:-      £P^  J»- 


f-l  tz:: 


^$ 


5=JL^ 


I  tztzr-  3i      p 

I  --^- 


--V        • 


HI-FKKKNCKS.      Wanner,  Tdnnht'iu.o'i:  1:21.  'JoG  ;    /-V//!////  Dutchman,  7.~>  (/>oro 
ritentitn),  100. 


44 


HARMOMC  ANALYSIS. 


Section  33.    Consecutive  Dominant  Sevenths.  Mark  each 

chord  according  to  its  apparent  key. 


75.     Andante  sostenuto  ussai. 

•4 


BIZET,  L'Arleaienne. 


-0-  1      -4- 

'  '  >*—    ^ -V 

REFERENCES.  Beethoven.  Op.  10,  No.  o.  Ill,  17  :  Op.  22,  II,  34;  Chopin, 
Prelude  No.  8,  in.  7  ;  Cramer,  Etude  IS,  HI.  9. 

Section  34.  Enharmonics.  Enharmonic  notation  is  the  use 
of  that  double  notation  which  may  be  applied  to  any  tone;  thus  E$ 
may  be  written  (lb,  or  K,  F^.  Enharmonics  are  used :  — 

1.  As  a  means  of  modulation  ; 

2.  As  a  means  of  simplifying  the  reading  or  playing  of  a 
passage,  which,  if  written  out   logically,  would  pass  through  a  re- 
mote and  difficult  key  ; 

3.  As  the  result  of  careless  or  wilful  notation. 

It  is  probable  that  no  feature  in  Analysis  causes  trouble  equal 
to  that  given  by  Enharmonic  Notation,  especially  by  that  careless 
and  illogical  kind  last  mentioned,  which  is  remarkably  common  in 
modern  music.  Countless  cases  exist  in  which  the  car  hears  one 
thing,  —  the  impression  of  a  key,  an  impression  consistent  and 
undisturbed,  —  while  on  the  paper  the  eye  beholds  another  thing — • 
two  contradictory  keys.  In  a  passage  in  sharps,  for  instance,  stands 
a  flat  chord,  and  the  mind  through  the  eye  is  aware  of  a  hitch, 
unwarrantable  and  without  reason,  while  to  the  ear  all  is  smooth 


HARM  OX  1C  AX  A  I.  Y  SIS.  45 

and  satisfactory.     Such  a  passage  will  oblige  the  student  to  find 
and  to  change  mentally  the  enharmoiiics  to  their  correct  and  legiti- 
mate notation,  if  he  would  account  for  things  satisfactorily. 
General  Rules  are  these  :  — 

1.  When  a  passage,  in  flats,  for  instance,  goes  into  sharps,  and 
stays  there  permanently,  the  chord  where  the  change  of  accidentals 
occurs  will  contain  the  tone  or  tones  enharmonically  altered;  in 
such  a  case  a  definite  modulation  is  made  and  is  to  be  recognized 
as  such  (see  Ex.  76)  ; 

2.  When,  for  example,  in  a  passage  in  sharps,  a  few  measures 
are  written  in  flats  and  are  followed  by  sharps  again,  this  passage 
in  flats  should  be  regarded  as  an  enharmonic  notation  of  the  sharp 
strain,  and  in  marking  it  two  methods  may  be  employed:  (a)  the 
chords  may  be  marked  as  they  appear  to  the  eye,  and  "  Enh.  Xot. 
of  such  and  such  a  key  "  be  added,  or,  the  letter  it-ai/,  (b)  the  chords 
may  be  marked  as  they  sound  and  hang  together,  not  as  they  are 
notated,  and  "  Enh.  Xot."  be  added  (see  Ex.  77)  : 

3.  When    an    occasional    contradictory    chromatic    intrudes,   it 
may  be  readily  changed  for  its  rightful  equivalent  by  spelling  the 
chord   in  question  and   finding  the  tone   foreign  to  the  scale  (see 
Ex.  79). 

In  marking  the  exercises  it  may  be  necessary  to  use  words 
instead  of  signs.  The  author  has  indicated  nborc  some  of  the 
exercises  the  question  the  scholar  is  to  ask  himself,  and  below  the 
manner  of  marking. 

o 

What  tones  are 

<-ha,iKe,l  SOU-BERT.    Son*. 

enharmonically  ? 


11 


G£  =  A? 
B-T  =  C  -> 


R-  ?  •  -'• 

'  "l  t_ '      x 


46  HARMONIC  ANALYSIS. 

77.     A  llegro  giocoso. 


i  BIZET,  L'Arle'sienne. 

What  key,  if 
written  iu  flats  ? 


78.     Poco  andantino. 


FRAKCK,  L'Orsraniste. 


'        X      ' 

\  \ 


-*- 


HARMONIC  ANALYSIS. 


47 


Does  this  chord 
belong  to  At>  ? 

79.     Allegro.      If  not,  which  is  the 
enharmonic  toue  '( 


,  Violin  Sonata 


ft: 


I         F.A. 


80.     Non  troppo  lento. 


FRANCK,  L'Organiste. 


^         & 

-* '-» 


~^- 


"^         I  M  • 

__^_     _f«^ 


81.     Moderato. 


WAGMJU,  Lohengrin. 


\ 


J 


48  HARMONIC  ANALYSIS. 

82.     Allegretto.  FRANCK,  L'Organiste. 


(E=fz=p=Q^=5i= 
Lii£s£^e=        I *~fti*~| 


HAR.MOMC  ANA  L  YSIS. 


'49 


KN'CKS.  Schumann,  Op.  12,  No.  2,  in.  17  ;  No.  8,  m.  1  ;  Chopin, 
Nocturne  No.  9,  in.  02;  Prelude  12,  in.  12;  Prelude  8,  in.  22;  Prelude  ID, 
m.  21,  Wagner,  Lohenyrin,  p.  14,  19,  22;  Tannhduaer,  144,  246;  Flying 
Dutchman,  41. 

Section  35.    Modulation  through  the  Six -Four. 


84.     Allcyro  inollo. 


BEKTIIOVKX,  <  >p.  7. 


RKFKKKXC'KS.     C'lmpin.  Polon;ti>i-  Xo.  3,  m.  -11; 


'iuniJii.in.-ter,  224. 


Section  36.  Assumption  of  Key.  A  modulation  may  be 
made  by  assuming,  taking,  a  new  key.  The  oluml  taken  may 
be  a  tunic  or  a  dominant,  preferably  the  former,  and  a  regular  pro- 
gression will  confirm  the  key  effect.  This  procedure  is  often  made 
in  sequence  form,  and  by  hitches  of  a  third. 


85.      Ml«jn>. 


A    '       t 


t  ~t: 


Srnriu'.HT,   Si 

-J~     -i     .-I- 


M5 


9  1 


50' 


HARMONIC  ANALYSIS. 


±g: 


=n£ 


gg 


r  r  ~r 


ir— fr-ite  Jg    r  n 

SE^pi^J 


P_^£E 


?»i 


^^T=F 


RKFKRKNCES.     Beethoven,  Op.  10,  No.  3,  I,  second  part,  m.  92;  Chopin, 
Prelude  9;  Wagner,  Tannhauser ,  pp.  7,  49,  245;  Flying  Dutchman,  36,  m.  13. 


Section  37.  Incomplete  Modulation.  A  progression  is 
sometimes  made  Lo  a  foreign  major  triad,  which  triad,  by  reason  of  its 
place  at  the  end  of  a  phrase  or  section,  holds  the  mind  in  suspense, 
and  thus  performs  the  function  of  a  dominant  harmony.  Although 
the  apparent  modulation  be  not  completed,  it  is  well  to  mark  such 
a  chord  as  modulatory,  including  as  many  of  the  preceding  chords 
as  may  rationally  belong  to  the  key.  This  kind  of  a  progression 
occurs  many  times  in  Wagner  as  a  vi  V,  or  IV  V.  Kemernber 
Principle  No.  5. 


86.     Allegro  ma  non  troppo. 
:r^=z^=  =S==^; 


^r?- 


SCHUBERT,  Quintet. 

**"j_        I  •* 

^E« 


i 


HARMONIC  ANALYSIS. 


51 


1 


=15*= 


-£= 


=^2*: 


?•- 


II 


RKFERKNCES.     Wagner,  Tannhauser,  124,  2:53,  231 ;  Flying  Dutchman,  3. 


Section  38.     The  Deceptive  Resolution. 


87.     Poco  animato. 


WAGNER,  Gctterdammerung. 


=z2i=i         =i 

1     H] 


^  -y^- -;:::ir 


52 


HA  RM  ONI  C  A  NA  L  YSfS. 


REFERENCES.  Beethoven,  Op.  7,  If,  2');  Chopin,  Prelude  No.  13,  ni.  15; 
Prelude,  Op.  4.~>;  Schumann,  Op.  12,  No.  8,  Coda;  Wagner,  Lohenyrin.  p.  51, 
m.  2;  also  pp.  64,  Go  ;  Tannhduxer,  pp.  4,  37,  146,  157,  256  ;  Flying  Dutchman, 
119,  227. 


Section  39.  Passing  Diminished  Seventh  Chords.  These 
usually  rise  or  fall  by  seconds,  major  or  minor,  most  often  the  latter. 
Composers  notate  them  very  irregularly.  The  roots  appear  here 
and  there,  as  is  shown  in  the  Examples  below,  and  often  in  a 
very  arbitrary  manner.  A  general  rule  of  notation  is  as  follows : 
When  these  chords  move  along  the  chromatic  scale,  every  fourth 
chord  should  have  the  same  root.  This  is  also  shown  below.  In 
phrases  of  this  nature,  no  firm  hold  is  felt  of  any  key,  except  at 
the  ends  of  the  phrase  or  section  —  everything  is  passing,  fleeting, 
which  lies  between  these  bounds. 

Mark  each  and  every  chord  according  to  its  notation,  or, 
what  is  better,  mark  the  chords  at  the  ends  of  each  phrase  or 
section,  and  pass  over  the  other  chords. 


88.      Laryn  <•  ine*ti>. 


BKKTHOVKV,  <  )p 


I 


HARMONIC  ANAL  Y.S/.S. 


*  See  Principle  No.  5. 


89.     Allegro  ma  non  troppo. 


,.  £,_       .0.  $f. 

__  _l_        TI^_    _        ^^ r^^V 

g,     *     5^         t  * 

— t.     t 


/^  -*& 

2* 


^      31 


RKKKKKNTKS.  Cliopin,  Prelude  ID,  in.  20  ;  Schumann,  Op.  ti.  No.  18; 
Bizet,  L'Arlc'firnne,  Suite  Nd.  1,  I.  I'n  [>»c<>  />iu  !cnt<>  :  Wagner,  Tanntiaitsa; 
pp.  5,  11,  47,  140,  -J:}8,  L'40  ;  /-Vv/m/  Dn'.-hnuin,  '2\:\. 


54 


HARMONIC  ANALYSIS. 


Section  40.     T!L«   Diminished   Seventh   on  the   Raised 
Fourth  Step. 

90.      Virace.  CRAMER,  Etude. 


RKFERKXCKS.  Beethoven,  Op.  10,  Xo.  2,  I,  40;  Cramer,  Etude  1, 
m.  19;  Etude  8,  in.  27;  Wanner,  Flying  Dutchman,  11,  123. 

Section   41.     Secondary    Seventh   Chords    in    General. 

Extended  successions  of  secondary  seventh  chords  often  give  trouble 
as  regards  the  definition  of  key.  Some  passages,  as  in  Exercise  91, 
when  shorn  of  the  passing  tones,  suspensions,  etc.,  which  form 
many  of  the  apparent  secondary  seventh  chords,  present  a  very 
simple  structure ;  in  which  case  the  analyst  must  decide  whether  or 
not  to  mark  all  the  combinations  as  real  chords.  Other  passages,  as 
in  Exercises  93  and  94,  present  a  series  of  secondary  sevenths,  often 
unmistakable  in  key,  which  turn  suddenly,  by  the  fact  that  any 
one  chord  may  belong  to  several  tonalities,  into  another  key,  possi- 
bly into  a  key  quite  remote.  And,  finally,  other  passages,  on  close 
examination,  will  !>e  found  to  be  made  of  alternations  of  supertonic 
seventh  and  dominant  seventh,  a  favorite  device  in  the  restless  music 
of  this  day,  especially  since  the  advent  of  Tristan. 

"When  used  in  succession,  or  in  clusters,  so  to  speak,  secondary 
sevenths  gravitate  toward  a  dominant  harmony  or  toward  a  super- 
tonic,  though  the  latter  case  is  rare.  This  leading  chord  defines 


II A  KM  OX  I C  A  XA  L  YSIS. 


the  key  of  the  preceding  chords.  Consequently  it  is  necessary,  as  in 
Exercise  93,  before  fixing  on  a  decision,  to  survey  the  entire  passage 
in  question  and,  having  found  the  dominants,  to  figure  from  them, 
to  possibly  reason  backward  to  the  first  and  opening  chord. 


91-     A  inlftntino. 


MENDELSSOHN,  Part  Song. 


— 

— 


--** 


L-     ._. 

.1 

/ 

92.     Allegretto.  '-KM,  Falstaff. 

'••«     *  _U>- 


e 


—  <*  'ill      P"*"*       ;t    I> 

3   **s ^--     L-  I  —  -   m       m   i  — ••••    -1 

^^gzrj^  -ff3»  •- «  g  • 

~/=^=*^S—  ::  •—    '  »^  " 


•$•050  , 


93.    A I /<•<;>•<>. 


Hi:i;rnnvr.N.  t  >[>.  10, 


:JLa   *   I  '„•   •     •  '5-i  Is 

^:ti    r       :*    *  ::  *    z!  K 

« — i — —> — i —  t_  „_.  r 

^ 


^ 
94.     .1 


r     r 


?  II 


1?.\.  ii,   Matt.    Pas.-i. 


r 


:   N, 

t 


UKFKUKXCKS.      Srliumaiin.  Op.  (>.  No.  4,  in .  oO :  O]\  f>.  Nos.  >,    l:>.  is.  1  : 
Cminor.  Ktude.  No.    1.  in.  l»i;   (Iriei;,  Op.   I'J.  No.  5;  Chopin.  Prehnl.',  No.  2. 


6  HARMONIC  ANALYSIS. 

Section  42.  The  Augmented  Sixth  Chords.  The  inver- 
sions of  those  chords  which  by  alteration,  and  before  inversion, 
contain  a  diminished  third,  and  which  after  proper  inversion  are 
known  as  the  Augmented  Sixth  (64),  the  Augmented  Six-Five 
(*+),  the  Augmented  Six-Four-Three  (J+Y  and  the  Doubly  Aug- 
mented Fourth  (4++  or  4-H-),  are  common  in  music  of  all  kinds  as 

3      ' 

harmonies  used  to  strengthen  the  key  impression,  or  to  enrich  the 
chord  structure,  or  to  produce  modulations. 

They  often  give  especial  trouble  to  the  scholar  in  Analysis,  — 
trouble  due  in  part  to  a  neglect  to  learn  the  chords  thoroughly  in 
the  Harmony  Course,  and  in  part  because  the  *+  and  the  4++,  through 
enharmonics,  are  used  interchangeably,  causing  confusion  to  the 
unversed.  To  illustrate  :  the  interval  of  an  augmented  sixth,  A**  F$, 
when  the  tendencies  of  its  tones  are  followed,  resolves  to  G  G,  the 
flatted  tone  falling,  the  sharped  tone  rising.  If  this  principle  of 
chromatic  leads  be  followed  out  strictly  with  all  the  chromatic 
tones  involved,  the  Augmented  Six-Five  —  A*7  C  E*7  F* — and  the 
Doubly  Augmented  Fourth  —  A^  C  D*  F& — will  resolve  to  different 
harmonies,  the  tone  Eb  falling  to  D,  or  being  held  over,  the  D$,  its 
enharmonic  equivalent,  leading  up  to  E.  But  composers  of  all 
schools  write  the  one  sound  in  two  ways  —  E^  or  D* — quite  as 
they  please,  and  carry  the  tone  up  or  down  regardless  of  rule  or 
reason.  As  already  said,  this  embarrasses  the  novice  in  Analysis. 

In  illustration,  examples  of  correct  and  incorrect  notation  will 
be  given.  It  may  be  said,  however,  that  cases  occur,  as  in  the  one 
quoted  from  Moxart,  where  the  6+  may  be  quitted  naturally  and 
most  sensibly  as  an  6+,  although  sounding  as  a  4+4  —in  which  case 
we  behold  a  simplification  of  notation. 

Find  the  root  and  write  the  proper  numeral,  and  then 
modify  it  by  the  proper  figures  and  accidentals. 


II A  RM  OMC  A  XA  L  YSIS. 


57 


c  J6        'V+ 


r,  ,          n",          iv  V 

6+  6^  x+ 

4+ 
3 


or:  C 


I  IV  Iio  iv 

6  046 

4  [SI]  5 

[S3]  [SIJ 


Sometimes  one  figuring  may  be  used,  sometimes  the  other. 


95.     Allcffrt)  moderate. 


t=          t 


SCHUBERT,  Song. 


?~«- 

*?/• 


T  4^ 

^:v- 

l 


96.     .\fjiiato. 


WAI.NKR,  Lohengrin. 


97.     Allfffrptln. 


KKANCK.   Violin  Sonata. 


^       H 


App. 


Jo        <n  ^1    =S«^ 

-    Jn^:: ftitz: 


58 


H A RM ONI C  ANAL} 'HI a1. 


98.     A  ndante. 


PACKNER,  Bohemian  Air. 


—  — 4—  -r 

~ 


, 

\\ 


99.     Andante. 
^\~ 


WAGNER,  Lohengrin. 


t    .-..- 


^ 

~r 


----•=q 


_j__  _« 


£T      ^ 


"^l 


I 


100.     . 


« 


o          --S-& 

^  ,     , 

-'S?    If     X3.-» 


MO/ART,  Don  Giovanni. 

1 J_J          I_S~~ 


r 


xp  xy — x?^ 


HARMONIC  ANAL  YSIS. 


59 


BEETHOVKX,  Op.  7. 


m 


REFERENCES.     6f  Beethoven,  Op.  '2,  No.   1.   IV,  S;  Op.    10,  No.  2,  II,   15; 
Wagner,  Lohengrin,  pp.  3,  ;">,  15  ;   Tannh<iust:r,  4. 

6+  Beethoven,  Op.  7,  I  ;  Chopin,  Prelmlf  1'J.  in    :50 :  Cramer.  Etude  17,  m.  19; 
5       Etude   19,m.  'JO;  Wagner,  Lotieni/rin.  pp.  9,    Hi,   50,    9:>.  1«I5.   1>9,   190; 
Tannhauser,  31,  ±2-1,  '2:39. 

6+  Beethoven,  Op.  1=5,  III.  4(3;  Chopin,  Prelude  '20,  in.  6;  Prelude  21.  in.  :{'2; 
**"  Schumann,  Op.  6,  No.  1,  m.  16;  Op.  15,  m.  2;  A\'agner,  Flying  Dutchman, 
3  162,  175. 

6+  Schumann,  Op.  0,  No.   14,  in.  28:  Op.  ti.  N'o.  17.  m.  31;    Chopin.   Polo- 

^+f  naise,  No.  1,  in.  :50 ;  Wagner,  Tannhauser,  58. 
o 

6r  a-s  4t+  Beethoven,  Op.  7.  I,  in.  98;  Wagner.  Lohenyrin,  pp.  12,  2^,  62; 
5  Flying  Dutchman,  128.  1:58. 


Section  43.  Modulation  down  a  Minor  Second  by  an 
Augmented  Chord.  The  V  ,  and  its  enharmonic  equivalents, 
the  s+  and  the  4++  (thus,  (1  b  d  1';  g  b  d  K:;  g  1)  C"  e-),  were  often 

O 

used  in  modulating  down  a  semi-tone  by  coni]>osers  oi'  Chopin's 
day.  The  progression  appears  to  have  become  hackneyed,  and  for 
a  time  abandoned,  to  be  revived  with  tremendous  power  by  Wagner 
in  his  Tristan. 

The  use  of  enharmonics  makes  the  analysis  at  times  a  little  ditli- 
cult  and  pu//.ling.  Measure  4  in  K.xercise  10:!  is  a  good  instance; 
in  some  editions  the  f«  is  adhered  to  throughout  the  measure  —  but. 
as  the  "  identity  of  a  chord  depends  on  its  resolution  "  and  this 
chord  goes  into  B  major,  it  is  a  K  major  chord,  altered,  and  nothing 
else. 


60 


HARMONIC  ANALYSIS. 


102.     Presto. 


i — i  — 
J=t$^ 


r  r 


^ 


--p^ — HI — I  — r 
=±^_^i=^=t.J8y_«_g- 

i      77        F      r 

III         II 

1    ^-^ 


CHOPIN,  Prelude. 

q-*!=q- 


*  * 

*==£ 


— h 


Ibid. 


• — f. 


^- 


=h 


UKI  i  UKNC  K.      Chopin.  FS  minor  Prelude. 


HARMONIC  ANA  L  YSIS. 


Gl 


Section  44.  Chords  with  a  Diminished  Third  or  Hidden 
Augmented  Sixth.  These  are  the  chords  of  the  preceding  section 
in  some  other  form.  The  Augmented  Sixth  may  be  found  in  any 
two  upper  voices,  or  its  equivalent,  the  Diminished  Third,  may  be 
present.  In  figuring  use  numerals,  and  accidentals  enclosed  in 
brackets  to  show  the  alterations. 


103.     A  llegretlo. 


FRAXCK,  Violin  Sonata. 


«J 

—  i  — 

—  t 

i 

5j  - 

-a=i- 

—  ¥~'  — 

—  &-.  — 

—  fe-L- 

^  .                    ?'  .  .  . 

HKKKKKNCKS.     Chopin,   Prelude   No.    4.  in.    2:5;   Prelude  17,  m.  20,   22; 
Prelude  22;   Wagner,  7'rinnh(i"!<er,  "2-'>\,  2o!».  240;    Flying  Dutchman  2,  22. 

Section  45.     The   Flat  Second   and   Sixth    Steps.     The 

first  inversion  of  the  supertonic  triad  containing  this  lowered  — 
the  Flat  Second  --step  is  commonly  known  as  the  Neapolitan 
Sixth.  Although  most  frequent  in  this  form,  this  altered  super- 
tonic  may  be  used  with  any  member  in  the  bass  and  in  either  mode, 
in  major  requiring  two  alterations.  It  may  be  used  at  the  begin- 
ning of  a  phrase,  often  misleading  the  student  (Principle  Xo.  5 
must  be  borne  in  mind),  or  in  its  course  ;  and  a  transient  modula- 
tion is  often  made  through  the  Neapolitan  Sixth,  or  without  it,  to 
the  key  of  its  root,  to  the  key  of  the  Flat  Second  —  sometimes  of 
beautiful  effect  —  which  key  is  quickly  abandoned  for  a  resumption 
of  the  reigning  tonic  key. 

SIGNS:   ii,  11°,         ii  ,         X  ,  ii.,  n 

' 


ii  , 

6' 


X  , 

6 


rbn 


or 


bi 


] 


The  Flat  Sixth  Step  at  times  occurs,  although  less  frequently 
than  the  Flat  Second  Step.     It  is  easy  to  recognize. 


62 


HA  RMOXfC  A  \A  L  YSfS. 


104.     A  llegro. 

I*-. 


WA<;XKR,  Flying  Dutchman. 
^ 


REFERENCES.  Beethoven,  Op.  27,  No.  2.  I,  21;  (meg,  Op.  6,  No.  4.  piii 
AUcfiro  :  Schumann,  Op.  6,  No.  .">,  in.  12  and  22  ;  Op.  68,  No.  29,  B*7  strain 
and  Coda;  Cramer,  Etude  3.  in.  2-1;  Etude  9,  m.  6,  60;  Etude  10,  m.  22.  - 
Sec  also,  for  modulation  to  Key  of  Flat  Second,  Chopin,  Prelude  Itj.  m.  7 
from  end;  Bizet,  L'ArlLxienne,  Suite  No.  l.II.  in.  29.  Flat  Sixth,  Wagner, 
Tamthauser,  p.  80. 

Section  46.  The  Flat  Seventh  Step.  Occurs  most  frequently 
in  the  minor  mode,  and  often  as  a  means  of  softening  the  harshness 
inseparable  from  the  augmented  second  formed  l>y  the  descending 
seventh  and  sixth  steps  of  the  harmonic  minor  scale.  It  is  apt  to 
mislead  the  student.  May  bi-  found  in  sequential  passages,  and  as 
the  root  of  an  independent  chord. 

SK;XS  :     V,    or     V  .     or      vn°,    etc. 

[73]  [73]  [?3J 


HARMONIC  ANALYSIS. 


63 


106. 


CRAMER,  Etude. 

K 


Section  47.  Embellishment  of  the  Tonic  Six-Four  in  a 
Cadence.  The  tonic  six-four  moves  most  naturally  into  a  dominant 
cadence.  The  suspense  attendant  on  this  six-four  chord  is  often 
heightened,  by  composers  of  many  schools,  by  embellishing,  so  to 
speak,  this  six-four  chord  before  its  resolution  into  the  dominant, 
by  harmonies  diatonic  or  chromatic.  Since  they  merely  intensify 
the  key  effect,  such  chromatic  harmonies  may  most  properly  be 
marked  as  altered,  i.e.,  as  non-modulating. 

The  same  procedure  is  at  times  made  with  the  dominant  chord. 

Examples  are  especially  frequent  in  the  works  of  Mozart  and 
Beethoven. 


107.      A  llt'fjro  con  !>ri 
>"V§--X      S       i 


BEETHOVEN,  Op.  10. 


64 


If  A  HM  OM  C  ANAL  YSIS. 


! 


Section  48.  Consecutive  Tonics.  Progressions  are  not 
unusual  which  may  be  explained  only  on  the  supposition  that 
consecutive  tonic  impressions  are  possible,  and  are  intended  by  the 
composer.  Such  progressions  are  generally  made  agreeable  by  the 
use  of  common  tones,  sometimes  enharmonically  expressed  ;  but 
cases  are  not  unknown  in  which  the  common  and  connecting  tone 
is  dispensed  with  altogether. 


108.     Allegro  molto  cicace. 

I     • 


GKIEC;,  Violiu  Sou.ita. 


Reduction. 


109.     Allegro  maestoso.         LISZT,  Concerto. 


REFERENCKS.     firieg,  Op.  6,  No.   3,  m.  34 ;  Cliopin,  Prelude  8,  m.   23; 
a'nor.  TtiHrihiitmrr.  '236.  in.  5. 


HARMONIC  ANALYSIS.  65 

Section  49.  Chromatic  Passing  Chords  and  Passing 
Sequential  Figures.  A  logical  outgrowth  of  passing  tones  in  a 
single  voice  is  the  union  of  several  voices  in  passing  chords  moving 
in  one  direction.  Furthermore,  as  two  single  voices  may  move 
from  one  consonance  through  contrary  motion  to  another  conso- 
nance, and  the  satisfactory  outcome  of  the  passage  may  compensate 
for  all  the  transitory  harshnesses,  so,  proceeding  logically  from  this 
premise,  modern  composers  have  made  bold  to  employ  chords  in  the 
same  manner. 

The  two  outside  voices  are  written,  and  any  combination  which 
seems  good  to  the  composer  is  used  in  harmonizing  each  tone,  the 
chord  being  usually  fitted  to  the  soprano.  Not  infrequently  the 
most  intolerable  dissonances  result  —  combinations,  indeed,  which 
may  not  be  reduced  to  thirds,  which  are  not  chords. 

On  the  other  hand,  such  a  passage  may  contain  successions  of 
the  most  ravishing  beauty  —  due  to  the  euphonious  setting  of  each 
individual  chord,  and  to  the  mental  surprise  and  to  the  delight  of 
the  harmonic  sense  at  each  unexpected  change. 

More  than  this,  the  extension  of  this  spirit  to  the  sequence 
sometimes  occurs  in  modern  music,  as  in  the  example  by  Bizet,  where 
on  an  organ-point  a  sequential  figure  —  its  motive,  a  chord  tone 
with  an  embellishment  —  is  carried  out  obstinately  through  the 
rising  scale,  its  principal  tone  at  times  consouating,  at  times  disso- 
nating  sharply,  the  whole  thing  ending,  however,  satisfactorily  with 
a  good  tonic  impression. 

In  marking,  much  judgment  must  be  used.  If  the  chords  be 
disconnected  but  yet  long  enough  to  give  the  ear  a  series  of  strong 
impressions,  then  they  will  fall  under  the  head  of  Consecutive 
Tonics,  with  possibly  two  or  more  occasional  chords  in  one  key. 
When  enharmonics  are  used  with  one  general  chord  or  key  impres- 
sion, the  task  is  to  fix  upon  the  places  where  this  impression  is  made, 
to  mark  them,  and  then,  as  these  places  govern  the  impression  of 
the  whole,  to  account  for  the  rest  as  best  one  may  —  passing 
tones,  etc. 


66  HARMONIC  ANALYSIS. 

110.     Andante. 


_Z(2 tT1^^ P^   P** 


WAGNER,  Walkiire. 

^J 


ziF=_f=:lz 


l-ffe=^SE  ESTEEM! 

l-l=:stzi£3-cfe—    —5-       -d 


-UU— 


si 


—  i      SM a 

=\-^ 

—*-«*}— 


"frgr-^p 


r**/^'     "    — ^d 1~^^ 

»=Bg: 


— t i-^r 

«>— 


is 


111.     yl  llegro  rivace. 


GrODARD,  Violin  Sonata. 
simili 


=1= 


1  i  i  I 


HARMONIC  ANALYSIS. 
112.     Tempo  ill  marcia. 


67 


£  m 

-, I       _    L. 


BIZET.  L'Arlesienne. 

K 


t         £ 


?*' 


-sr  -la- 

P 


£    £    f:    * 


£— 


=t=t= 


^ 


L 


PS=S3? 


i|y^_j^^grffc=i  -  ^-  -  ^         ^j^rquq 
,__,       _^jft^=        _^_ 


i 


r^-^ 


S 


^.         A 

— t t--. 

'      I^J 


|. 


"-4- 


113.     Allegro  molto. 


WAGNER,  Tristan. 


t— 


68  HARMONIC  ANALYSIS. 

Section  50.  The  Sequence  is  the  continuous  transposi- 
tion, more  or  less  regular,  of  any  group  of  notes  or  chords, 
and  consists  of  a  Motive,  or  Model,  and  Repetitious,  or  Trans- 
positions, of  this  Model.  These  transpositions  may  be  one  or  more 
in  number,  and  the  Sequence  may  be  diatonic  or  chromatic  through- 
out, or  a  mixture  of  the  two,  or  may  modulate. 

When  diatonic  —  when  based  on  the  notes  of  the  key  in  which 
it  begins  —  and  when  carried  out  far  enough,  the  diminished  or 
augmented  chords  of  the  key  cause  harshnesses  which  are  more  or 
less  marked  according  to  the  position  of  the  dissonances  involved. 
These  harshnesses  add  to  the  interest  of  the  Sequence,  and,  as  is 
usual,  may  be  compensated  for  by  the  outcome  of  the  whole  passage 
in  bland  principal  harmonies. 

In  a  modulating  Sequence  of  some  length,  especially  in  instru- 
mental music,  composers  often  raise  or  lower,  arbitrarily,  some  tone 
in  an  occasional  Repetition.  This  causes  an  irregularity  which,  by 
breaking  the  monotony,  adds  to  the  interest  of  the  whole.  These 
irregularities,  interrupting  the  continuous  rise  or  fall  of  definite 
keys,  often  produce  what  the  author  calls  sham  keys ;  for  while 
the  roots  of  an  apparent  dominant  and  tonic  may  be  present,  the 
tones  which  go  with  them  do  not  form  the  intervals  which  charac- 
terize these  chords,  and  the  impression  on  the  mind  may  be  defined 
as  that  of  a  key,  but  marred  in  some  way,  strikingly  incomplete. 

Furthermore,  a  sequence  may  be  based  on  a  succession  of  pass- 
ing thirds  or  sixths  ;  or  on  a  long  sequential  passage  made  up  of 
several  different  Motives  with  their  Repetitions. 

The  interval  of  transposition  depends  on  the  will  of  the  com- 
poser. The  Sequence  may  rise  or  fall  by  seconds,  may  move  by 
fifths,  and  may  go  up  or  down  the  chromatic  scale  on  the  basis  of  one 
sustained  chord  (see  Cadenza),  in  which  case  some  of  the  Repetitions 
will  move  about  or  on  foreign  tones  —  in  other  words,  the  essential 
tone  of  the  Repetition  may  be  a  passing  tone. 

To  mark  Sequences :  Xo  fixed  rule  can  be  given ;  the  nature  of 
the  passage  must  be  considered.  It  is  thought  that  lie  who  reaches 
this  point  in  the  book  will  be  able  to  use  his  learning  and 
judgment  rightly. 


HARMONIC  ANALYSIS.  69 

114.     Alia  Polacca.  Hi  MMI;I.,  I'oluiiai^e. 


-1  --*      «&«.       JL-         '--* 


i. 


a* 


03F^    ^ 


Reduce. 


* 


^  •_£*?."'  ?-~S"f .  *::j£l 


,    I 

19 


II 
II 


70  HARMONIC  ANALYSIS. 

115.     Allegro  brillante.  App.  CRAMER,  Etude. 


Where  is  the 
sham  key  1 


C  I 


117.     Knew/tea  ma  no»  troppo  Allegro. 


RINDING,  Violin  Suite. 


1 


Reduction  of  climax. 

?-_~-a    3      I    ^:^.-; 


- 

— 


_i_         _  zj=q 


>      -S*      --^=£-1*0-    -£--£- 


&    I    £-^ 
L_ , 


-us? 


HA RM 0 A7 C  ANAL YSIS. 


71 


118.     Allegro. 


W-*— d~«  -  m  -*— I  -"*-  i-^-J— -  i    ^  J  ~ 1  -=': 

^e. — « —  *-  4  9   j  9  jj^  — *1J*~* — -!-•-»-• — ' 


II 


RKFERKXCES.  Beethoven,  Op.  10,  No.  1,  I,  32  ;  Chopin,  Prelude  9,  in.  0  ; 
Prelude  20,  Prelude  21,  in.  32;  Cramer,  Etude  5,  in.  23;  Etude  1;  Etude  8, 
m.  13;  Etude  14,  in.  2(5;  Schumann,  Op.  G.  No.  2,  m.  7. 


Section  51.  Two  Simultaneous  Harmonies.  Cases  occur 
occasionally  in  modern  music  in  which  two  distinct  harmonic 
bodies  are  used  at  one  time,  the  one  over  the  other.  \\.  may  be 
possible  to  define  the  upper  chord  as  composed  of  foreign  tones,  or 
it  may  be  necessary  to  define  it  as  an  independent  regularly  resolved 
harmony. 


119.     A 


WA<;XER,  Gotteniammerung, 

^-       *% 

I  ^  ^  d 


72 


HARMONIC  ANA L  YSIS. 


J  +  f 


-BP- 


r, «  —  ^ — I  — 


lix. rK.isKNCK.      H'zt^t,  L'Arlv'fienne.  Suite  Xo.  2.  I,  ending. 


HARMONIC  AXALYti/a.  73 

Section  52.  The  Skip  Resolution.  The  normal,  the  strict, 
resolution  of  a  chromatic  tone,  and  of  three  members  of  the  V  and 

7 

of  the  subordinate  sevenths,  and  of  all  of  the  members  of  the  lead- 
ing tone  sevenths,  major  or  minor,  is  by  moving  a  second.  To  the 
violation  of  these  strict  resolutions,  modern  music  owes  some  of  its 
most  startling  progressions.  The  principle  is  simple  ;  the  one  lined 
F  *,  for  instance,  instead  of  going  to  the  one  lined  G,  is  carried  to 
some  other  tone,  the  rightful  tone  of  resolution,  G,  appearing  in  some 
other  voice,  above  or  below.  This  procedure  causes  a  dislocation 
of  the  resolution  ;  and  it  is  also  often  responsible  for  a  progres- 
sion which  not  only  startles  the  ear,  but  bailies  the  ear  in  ear- 
analysis,  and  may  be  made  out  only  through  examination  with  the 
eye.  A  chromatic  passage,  in  itself  closely  united,  correctly  written, 
and  consequently  stout  in  its  coherence,  is  by  this  means  torn 
asunder,  and  the  rightful,  the  primary,  phrase  may  be  found  only 
when  the  passage  is  rewritten,  and  the  voices  resolved  by  rule,  an 
F5  moving  a  second  to  G,  an  KK  to  I).  Cases  occur  occasionally  in 
which  a  hitch  becomes  necessary  even  in  this  Reduction.  More- 
over, enliar monies  may  complicate  the  affair,  and  cross  relations  are 
exceedingly  common. 

In  marking  passages  of  this  sort,  the  chords  should  be  figured 
as  they  stand  in  the  original,  and  the  phrase  may  be  reduced  in 
writing  to  the  primary  form.  The  legitimacy  of  this  primary  form, 
so  called  by  the  author,  is  well  shown  by  Kxercise  Xo.  120,  the 
outcome  of  the  first  four  measures  in  the  diminished  seventh  of 
C  minor,  toward  which  the  whole  progression  tends,  being  most 
satisfactory-. 


HARMONIC  ANALYSIS. 


120.     Presto. 


WAGNEK,  Tristan. 


r     -T^    H        I 


Original. 


«==!= 


=3=£ 


H3£ 


Reduction. 


121. 


SCHUMANN,  Op.   12. 


:^^_- 

LZLZji-rl— • 


*  ZI=|— I^ZZ =^     I 


Reduce. 


S^^gffg^t^^^ 
•  t  — *   P  -     iB7^^ 


122.     Moderato  e  ritenuto. 


WAGNP:R,  Tristan. 


i — 


HA  /? J/0A7 C  /I  AM  L  YSIS. 


75 


Section  53.     The  Church  Modes,  and  Unusual  Cadences. 

The  Church  Modes  may  be  defined,  briefly,  as  scales  in  which  the 
customary  order  of  semitones  is  changed.  These  alterations  often 
make  the  ordinary  cadences  impossible,  and  produce,  moreover, 
progressions  which  startle  the  harmonic  sense  accustomed  to  the 
modern  major  and  minor  modes  or  scales.  To  treat  this  matter 
exhaustively  is  needless;  the  bounds  of  this  work  also  forbid  the 
presentation  of  material  sufficient  to  teach  the  many  tine  distinc- 
tions between  the  several  Modes.  The  quickest  and  the  best  way 
is  to  regard  such  successions  as  triad  progressions,  pure  and  simple 
-  which  in  reality  they  are  —  and  to  mark  them  as  such. 

Place  as  many  chords  as  possible  in  one  key.     Xo  better 
rule  can  be  given. 


123.     Puco  lento. 


PiMi 


DVORAK,  Requiem. 

=a-i^ 


124.     Am/ante. 


Ibil. 


UKKKKKM  K.      Wa^nor.  Tnnnhiiuser.  L'.'iO. 


76 


HARMONIC  ANALYSIS. 


Section  54.  Two-part  Writing.  May  be  divided  into  two 
classes : 

1.  A  melody  in  either  voice,  with  a  broken  chord  accom- 
paniment ; 

2.  Two  equally  important  parts  or  voices.    In  the  former 
case  the  chords  are  dissolved  in  the  accompaniment,  and  though 
they  are  at  times  invested  with  foreign  tones,  they  are  so  plain 
before  the  eye  that  no  example  is  needful  here.     In  the  latter  and 
more  difficult  case,  the  most  essential  members  of  the  principal 
chords,  and  those  chromatic  tones  which  define  the  modulations, 
must  be  sought  for,  must  be  picked  out.     It  should  not  be  forgotten 
that  a  chord  may  be  dispersed  over  several  counts  in  the  measure, 
and  that  in  many  a  rapid  passage  it  is  the  sum  total  of  a  number 
of  notes  which  gives  the  chord  impression,  if  the  chord  be  dissolved. 

Generally  by  playing  simultaneously  those  tones  which  define 
the  chord  structure,  Two-part  Writing  may  be  resolved  to  fairly 
complete  harmony,  although  sometimes  badly  disjointed  in  the 
resolutions.  In  deciding  on  modulations,  the  tempo  must  be  borne 
in  mind.  It  is  well  to  remember  that  the  principal  chords  pre- 
dominate, in  order  that  the  key  effects  may  be  strong  and  unmis- 
takable. 


CRAMER,  Etude. 


inciple  14. 


HARMONIC  ANALYSIS.  77 

126.     Moderate.  CKAMKR,  Etude. 


127.     Molto  Allegro. 

u~5^3 — -^•••i 

L^kzrSH 


Jit*- 


^^=T=TJ^-'-4=^"4=F=  S_J__i-jr^j^.::^;-| 

P^^^^E^EtfeE§-~^d 


*      * 

f-        •&» 


P=F==Pq 


i^^^T'-^'  5  5:"F££  tTeS 

L:S=          Sz»-     Ett 


Section  55.     One-part  Writing  and  the  Cadenza.     They 

appear  in  various  forms  : 

1.  As  the   ornamentation  of  one  single  and  prolonged 
chord,  usually  the  tonic  six-four  or  the  dominant : 

2.  As  the  investment  in  foreign  tones  of  a  plain  chord 
structure,  easily  picked  out ; 


78  HARMONIC  ANALYSIS. 

3.  As  the  sequential  ornamentation  of  a  chromatic  scale, 
moving  generally  above  one  single  chord ; 

4.  As   the    sequential    development  of  some   harmonic 
motive  of  several  members,  sometimes  readily  denned,  again 
difficult  of  explanation,  although  clear  in  its  outcome. 

The  marking  must  follow  the  characteristics  of  the  passage. 
No  definite  rule  may  be  given  applicable  to  all  cases.  Following 
the  above  classification,  these  general  ideas  are  suggested : 

1.  Fix  on  the  chord,  mark  it  once  below  the  staff,  and  then  give 
each  foreign  tone  its  sign  ; 

2.  Define  the  chords,  and  then  mark  as  in  No.  1  ; 

3.  Fix  on  the  motive  of  the  sequence  and  mark  it,  and  then 
mark    those  principal    notes,  so-called,  over   which    the   sequence 
moves,  whether  they  be  chord  tones  or  foreign  tones,  the  unessential 
tones  in  each  transposition  of  the  figure  being  marked  only  in  the 
motive  or  model  (see  Sequence) ; 

4.  Define  and  mark  the  motive,  with  its  possible  modulations, 
and  then  follow  the  working  out  (the  task  will  be  simplified  if  a 
bracket  be  drawn  over  the  motive  and  over  each  repetition). 


128-     Animate.  CHOPIN*,  Nocturne. 

I 


S§ffi£  V'  h=»"3^-=-^ 

^?B^Hg^=P        E^E 


i — r    i     i 

4     4      4      4:     J 

z       :: 


HARMONIC  ANALYSIS.  79 

129.     Allegro.  BEETHOVEN,  Op.  10. 


--< 


-g r-\ 


1 —  — I a • — W~T~ 

— TT —  -i — ^^^^m — •  — I *-*-h- 


-Mr* — 3  *9 —  i  -  0 —     ^-5* —  j—  f — 
0    jj       f^ 


MH  — *— *— HJ*— ' 

;---»—[ 


:>: 


=5^^3 


& 


130.     yl  llegretto. 


CHOPIN,  Nocturne. 


8/-a. 


i       ^     *      .<^   gs 


80 


HARMONIC  ANALYSIS. 


Kva 


131.     Molto  allegro. 


Section  56.     Reduction    (continued') ;   its   Application   in 

Memorizing  and  in  Sight  Playing.  One  purpose  underlying 
the  writing  of  this  book  was  that  of  making  Playing  by  Memory 
and  Playing  at  Sight  easier  to  learn  through  an  application  of  Har- 
monic Analysis.  Although  the  bounds  here  are  too  narrow  to  allow 
an  exhaustive  discussion,  it  is  thought  that  the  student  may  be 
shown  how  to  command  his  material  and  heighten  his  usefulness. 

In  studying  thus  far  lie  will  have  seen  that  all  music  is  either 
plain  or  figurate,  and  that  a  piece  of  tigurated  music  is  always  built 
on  a  plain  harmonic  structure.  He  must  have  learned  that  this 
harmonic  structure  is  a  concrete  thing ;  that  it  may  be  taken  hold 


HA  KM  OX  1C  ANALYSIS.  81 

of,  as  it  were  ;  may  be  played  by  itself,  giving  a  good  idea  of -the 
whole.  He  must  have  begun  to  realize  that  in  playing  from 
memory  there  is  given  to  the  player  a  greater  assurance,  if  he  knows 
that  at  a  certain  point  he  is  to  use  such  and  such  a  chord,  or  to  go 
to  such  a  key,  or  that  a  certain  cadence  begins  with  the  Neapolitan 
Sixth  — than  if  he  does  not  know  it.  It  costs  him  no  unusual  effort 
to  remember  this  Neapolitan  Sixth ;  no  more  than  it  costs  him  to 
remember  that  going  down  a  certain  street  Mr.  Y.'s  house  will  be 
passed  before  Mr.  W.'s.  The  effort  was  needed  in  learning  to  know 
and  to  recognize  in  the  first  place  thin  especial  chord  ;  when  once 
learned  it  became  a  part  of  the  mental  furniture,  ever  ready  for  use. 

Experience  shows  that  when  a  piece  of  music  is  committed  to 
memory  through  a  knowledge  of  the  harmonic  structure,  there  is  a 
certainty  of  performance  unknown  when  the  piece  is  committed — as 
is  usually  the  case —  by  many  repetitions.  In  this  latter  instance  — 
that  of  many  repetitions  —  automatic  impulses  are  made  on  the 
sub-consciousness  ;  impressions  on  that  part  of  the  nervous  system 
which  controls  habitual  acts ;  and  experience  shows,  also,  that  if 
in  performance  anything  happens  to  disturb  the  performer,  or  if, 
as  is  often  the  case,  the  physical  forces  perchance  take  an  ebb,  the 
thread  is  suddenly  broken,  and  a  repetition  of  the  piece  will  cause, 
generally,  according  to  what  seems  to  be  a  law  of  the  mind,  a 
second  break -down  at  the  self-same  place  —  a  thing  some  of  our 
readers  may  possibly  have  observed. 

If,  however,  to  these  impressions  stored  in  the  sub-consciousness 
through  many  repetitions,  there  be  added  impressions  stored  in  an- 
other way  and  on  the  consciousness,  namely,  volitional  impulses, 
subject  to  the  call  of  the  will  in  its  demands  on  the  motor  nervous 
system  —  as  is,  for  instance,  the  mental  picture  of  a  certain  progres- 
sion occurring  in  a  certain  place  —  then  the  surety  of  jterformance 
in  playing  from  memory  is  heightened  very  greatly  :  for  these  two 
parts  of  the  human  make-up  will  play  the  one  into  the  oilier;  the 
one  will  help  the  other;  and  the  chances  are  that  where  the  one 
fails  the  other  will  be  ready  to  carry  on  the  process.  Too  much 
stress  cannot  be  laid,  then,  on  making  an  effort  to  iiieniori/.e  through 
a  knowledge  and  use  of  Harmonic  Analysis. 


HA  RM  OMC  A  NA  L  YSIS. 

The  piano  player  must  know,  for  instance,  the  keys  which  mark 
the  beginning  of  each  strain  he  is  to  play.  If  there  is  a  peculiar 
progression,  this  he  must  know  thoroughly ;  for  example,  it  will 
help  him  in  memorizing  Chopin's  Eighth  Prelude  to  know  that  in 
the  eighth  measure  the  figure  moves  down  the  chromatic  scale 
through  successive  dominant  sevenths,  and  that  at  the  end  of  this 
group  is  a  dominant  seventh  chord  with  a  suspended  root  in  the 
bass,  and  occupying  not  one  count,  like  the  other  chords,  but  two 
counts.  This  seems  much  to  remember.  If  the  habit  has  been 
formed  of  thinking  of  such  things,  it  is  little.  For  after  some  prac- 
tice the  student  will  be  able  to  keep  such  matters  in  his  mind  and 
to  help  himself  as  he  plays,  and  the  mental  habit  once  started  will 
grow  readily.  And  if  he  says :  "  This  savors  of  pedantry,"  let  him 
remember  that  of  such  minutiae  are  pieces  of  music  made.  A  good 
artisan  cannot  be  unmindful  of  the  material  in  which  he  is  work- 
ing ;  nor  can  the  musician.  He  is  not  to  remember  every  tone, 
every  little  tone.  The  sub-conscious  part  of  his  nervous  system  does 
that ;  and  a  wrise  provision  of  nature  it  is,  too.  He  is  to  learn,  first, 
to  remember  a  few  details  and  to  hold  himself  in  readiness  to  pro- 
duce them  as  he  plays  —  a  series  of  rising  diminished  sevenths,  or  a 
sequence.  After  a  time  his  mind,  through  the  motor  nerves,  the  will 
part,  will  stand  ready  to  assist,  as  said  before,  and  by  looking  ahead 
and  seeing  those  features  which  it  has  grasped  and  retained,  will  give 
him  a  number  of  guiding  points,  beacons,  by  the  way.  We  can  only 
say,  in  closing  this  portion  of  our  discussion,  that  it  is  wonderful 
how  well  and  easily,  how  surely  and  quickly,  the  mind  will  begin 
to  work  if  this  sort  of  thing  be  practised  regularly  and  persistently. 

Going  farther  in  our  contention,  it  is  a  wonderful  help  to  the 
sight  player  if  in  a  piece  of  figuration  lie  is  able  to  see  through  the 
mass  of  notes  and  to  behold  the  backbone,  the  framework  of 
the  whole  affair.  He  will  then  possess  a  grip  on  the  piece;  he  will 
play  with  an  ease  and  a  surety  unknown  to  that  sight  player  who 
regards  the  ma/e  of  printed  notes  as  mere  signs  which  his  eye  must 
see  and  decipher,  perhaps  painfully,  in  their  succession,  and  which 
his  fingers  are  to  interpret  one  after  the  other.  There  is  such  a 
thing  as  "  ihe  Glance."  Tt  is  possessed  in  greater  or  less  degree  by 


HAKMONIC  ANALYSIS.  83 

all  good  sight  readers.  In  its  lowest  form  it  is  a  natural  gift  unac- 
companied by  any  knowledge  of  harmony,  and  those  who  possess  it 
are  able  to  read  music  within  their  technical  skill  without  hesita- 
tion. This  group  is  a  small  one.  A  larger  group  is  that  formed  of 
those  of  more  or  less  theoretical  knowledge  ;  it  contains  those,  for 
example,  who,  on  seeing  a  group  of  notes  such  as  that  in  Exercise  16, 
recognize  the  chord  and  play  it  as  a  chord,  as  a  form  of  arpeggio. 
Such  a  player  has  an  enviable  advantage  over  him  of  the  first  group. 
This  group  is  a  large  one.  We  place  in  the  third  group  those  who 
with  great  natural  gifts  have  by  long  study  reached  the  end  of  sight 
playing,  in  the  shape  of  playing  from  the  modern  orchestral  score. 
This  is  a  possession  attained  by  comparatively  few.  It  is  to  the 
middle  class  that  we  now  speak. 

Aside  from  the  great  advantage  over  the  natural  sight  player 
possessed  by  him  who  can  look  at  a  chord  passage  and  read  and  in- 
terpret it  as  a  whole  —  as  in  the  case  of  Exercise  16,  mentioned  above 
—  there  is  an  element  little  made  of  in  general  teaching,  which,  if 
carried  out  far  enough,  will  produce  excellent  results  —  that  of 
playing  a  Reduction,  of  seeing  the  chord  structure  as  one  plays  the 
actual  notes  before  him. 

And  as  material  well  fitted  to  give  one  this  mental  habit,  we 
recommend  the  Fifty  Selected  Studies  of  Cramer.  We  add  below 
Examples  showing  how  these  Reductions  should  be  made,  and  a  List 
giving  the  order  in  which  they  may  be  practised.  It  will  be  seen, 
on  studying  the  Examples,  that  the  voices  must  be  kept  in  vocal 
compass,  and  should  be  quietly  led,  although  occasional  breaks  in 
the  leading  may  be  unavoidable  in  the  compression  of  a  very  florid 
structure.  These  reductions  should  be  played  over  and  over  until 
they  are  easy  and  a  habit  has  been  formed  which  enables  one  to 
see  the  framework  in  playing  at  sight.  In  other  words,  one  must 
learn  to  play  chords,  ami  we  suggest  that  the  practice  of  this  tiling 
be  persevered  in  until  <  nc  has  acquired  a  masterv.  It  will  be 
found  profitable  to  practise  in  this  way  on  pieces  of  all  kinds. 

LIST.  Xos.  2.  :).  (i.  n.  10,  17.  20,  M,  24,  27.  2*.  -\7.  38.  41.  14,  easy,  the 
chord  element  being  plain  to  the  eye;  1  .  f>,  S.  IS.  21,  2ti,  :>r».  JVJ.  47.  1!',  :'>!), 
34.31,40,22,4.  more  difficult:  these  contain  sequences  and  figuration  more 
or  less  involved. 


84 


HA  HMON1 C  A  .\A  L  YSIS. 


REDUCTIONS   OF   THE   CRAMER    STUDIES. 


132.     Allegro. 

Study  No.  1.  meas.  10. 

<-&- 


meas.  13. 


No.  5.  meas.  23.  No. 


No.  8,  meas.  13. 
•       ' 

-r^ 


;   II 


$» 


1     '  I|p 


-^ —    -—• fr— 


I 


^No.  1.3.  _^T 

^ 


f-  f- 

~7}       !         h    ^t: 

*  th— 

*'Hi 


fe^s-ss 


__) 


m 


:r^         ii-H 

E£E 


No.  20. 


No.  21. 


f  10  ZJ  .^-^71     a 

12  x>:rS^i    ?• 
=:fc^±z:i2h*z 


^Tgrmffg 


No.  26. 


?* 


^1 

-i — 1_-« 


^ 


^^'s---^^'.^ 

No.  27. 


No.  37. 


i  r-^-S^-n 


^W§sr\        ±2^5  [-* 

z4~|r_zJi=i"iril:_  _  *Tti"^_:-«z^         _T»_!  ~_ 


HA  RMON1C  ANA  L  YSIS. 


REDUCTIONS  —  TO   BE   WRITTEN. 
133.     Anrlante.  FUANCK,  L'Orgam'ste. 


: 


I 


(?••-     -*- 


134.     Moderate. 


SCHUMANN,  Op.  15. 


135.     Allegro. 

rJ-          -4- 


WAGNI.H,   Flying  Dutchman. 

^i;=Fr-fc 


__l_— 
-& 


i:& 


f 


___ •*•*••  • 

>g:7    ^  .q  ^.--:-^--_;j  5^,1 — ^--frj  *  '*  *     \  2~"f[ 

[:*S  ;  J.  5_j  ;  g:. 

^  ,     ^>  v  L^  .      -,     3-^-:     ^   ,J  *  * 


czi^'i  ^"'i 


86 


It  A  KMO.\/r   A  AM  L  YSfS. 


136.     Piano  agitato. 


MENDELSSOHN,  Song  without  Words. 


-t   —«!*— 


S    J 
, — _ — i — 


UARMOMC   ANALYSIS, 
Reduction. 


87 


j— 4 

'      


=F 


137. 


CHOPIN,  ljrelude. 


o      +    D.  App. 


-          : 
f  -  E* 

^ 


IT  .  t  ..- 
-^H 


ri    .* 


I— &  t 


In  the  original  the  left  hand  doubles  this  right-hand  part  in  the  lower  octare. 


88 


HA  RMON1C  A  NA  L  YS/S. 


Section  57.  Full  Table  of  Signs.  A  capital  letter  shows  a 
-major  key  ;  a  small  letter  shows  a  minor  key  ;  a  large  Roman 
numeral  shows  a  major  triad,  and  a  small  Roman  numeral  a  minor 
triad.  The  sign  +  shows  the  augmentation  of  a  triad,  and  the  sign  ° 
the  diminution  of  a  triad. 


Triads  in  Major. 
I 

II- 
III 

IV 
V 

VI 
VII° 


Triads  in  Minor. 
I 

III+ 

IV 

V 
VI 
vn° 


The   inversion  of  triads  and  of  seventh  chords,  both  principal 
ami   subordinate,    will    be    indicated    by   the   customary  figurings  : 


66644    attached  to  the  respective   Roman  numerals.     Or,  the 

'    4'    5'    3'    2' 

letters    a.   I, 


d,    meaning    root-form,    tirst,   second,    and    third 


HARMONIC  ANALYSIS.  H9 

inversions,  may  be  used  with  these  same  numerals  ;  thus  :  I     I     I 

7         7          7  +  -  a'      b'      c* 

na'  Hh'  Hc'  T11,,'  HIC>  etc-     The  diminished  seventh   chord,  in   its 
various    forms,   will  be   marked:   vn°  ,   vn",    vn°,   vn°,   or:    vn°7° 

070  070  070  7°  6  4  4'  a 

VII        ,  VII        ,  VII       .  5  3  2 

be  <i 

Altered  Chords.  These  may  he  indicated  by  writing  below 
the  proper  Roman  numeral,  and  the  sign  of  inversion,  if  there  be  an 
inversion,  figures  accompanied  by  the  proper  accidentals,  these  being 
placed  in  brackets.  Thus,  n°,  means  :  supertonic  six-five,  with 

pfj 
diminished  fifth,  and  sharp  third. 

The  Appoygiatura,  A  pp.  ;  'Double  or  Triple  Appoyyiatura,  I). 
or  T.  A  pp. 

The  Appogyintura  Chord,  App.  Chd. 
The  Free  Tone,  F.  T. 

The  Accented  Pdssiny  Tone,  0;   the  Unaccented  Passing  Tone  +. 
The  Embellishment,  K 

The  Embellish  iny  Chord,  K.  Chd.,  or  K.  Chd. 

VI 


The  Suspension,  S. 

The  Anfi'cijHiliou,  \. 
The  Free  Anticipation,  V.  A. 
The  Retardation,  \\. 

The   Onjoii  l\>int  :  Tonic,  T.  O.  P.  ;  Dominant,  IX  (\  V.  ;  Medi- 
ant. M.  O.  I'.;  Double,  Dbl.  (  ).  P. 

Section   58.      Special    Remarks    to    the    Teacher.      The 

value  of  this  course  of  instruction  may  possibly  U>  heightened  bv 
the  following  application:  The  text-book  is  used  as  a  book  of  refer- 
ence ;  the  teacher  selects  a  piece  of  proper  ditliculty,  —  sav,  for 
those  who  have  worked  through  Part  I  and  Part  1  1,  the  P.eethoven 
Piano  Sonata,  Op.  10,  No.  '2,  movement  I.  and  directs  the  class  to 
give  attention  in  analy/.ing  to  the  following  features  which  occur 
in  the  movement  :  Suspensions.  Appoggiaturas.  Altered  Chords, 


90  IIARMOMC  ANALYSIS. 

Sequences,  Augmented  Chords.  This  procedure  focusses  the  mind 
on  certain  definite  features  and  makes  the  work  of  learning  very 
direct;  it  also  gives  the  student,  generally,  several  examples  of  the 
same  thing,  —  several  Suspensions,  for  instance. 

To  lay  out  a  course  in  this  line  would  be  difficult.  The  judg- 
ment of  the  teacher  must  be  called  into  play,  and  a  certain  amount 
of  this  work  will  be  very  beneficial.  Hut  it  should  not  cause  the 
student  to  neglect  the  General  Exercises  in  Part  IV,  which  contain 
characteristic  and  individual  passages. 


PART    FOUR. 


Section  59.     General  Exercises. 

138-     .  I  llvyretto. 


SCRIAIUXE,  Prelude. 


r^Z  :3  r---   I    J  -4 

t        •«* 

~-=ii*-*" 


2rj ?« •- 


I        I 

-• •---    "• 


**  5»_ 


->*:*  -i  »* ,n 

\  ".I.."  &'-'*- 


92 


HA  RM ON  1C  ANAL  YSIS. 


139.     .1  dagio  con  molto  espressione. 


GOI.DMARK,  Violin  Suite. 


;+ 

t* 


-=— 9- 


II 

rrv 

If 

\       ^ 

—..                           -<^- 

1         if*L«                  ^*                   ^«                                   >*                                                                                  >* 

-(£*-               -0- 

M         m          m         \      "^          f'&\+* 

i  *f  j        1  1 

,                ,      \            5_Z1          ^ 

'-•*'      1 

*^  ^                            9^9 

#J       -                          <>     1          * 

'  /o       1    2 

^ 

5*      •      »      1            r      1 

*i^  5'    t 

T        r       f        f 

^^ 

140.     Vh-ace. 


Cnoi-iN,  Valse. 


HA  KM  ON  1C  A  NA  L  \'SIS. 

£*• 


93 


4    J.  4  -'- 

*     t  -?—T- 


141.     . 


WAGNER,  Gotterdamrnerung. 

i^s^S' :  ~2* 


=V*' 

r.x>-  * 


94 


HA  HMOM<  •   ,1  .V/l  /,  YSIS. 


:..  fr-L    =Wtr-l-rtr-k—  — r— f^-     -?+Xjz 

r^_.j^=^— ^z  zq^aSc 

-?  LaLJ    tmu 

^ 1/  -£>-  -*• 


142.     Allegro. 


J.    WIHTOI.,  Prelude 


: 


111 


— si-^— X— 


HA  RMONI C  A  .VA  L  YSIS. 


143.      .  1  llff/rello. 


I.M;,  Violin  Suit,- 
»_     -*.       *.  . 

~sZ± 


— J  - 


« 


S,  H' 


75?  :  i 

5*  r— 


HARMONIC  ANALYSIS. 


144.     Ziemlich  schnell  (poco  Allegro).          K.  STRATSS,  Song,  Op.  49. 


HARMONIC  ANALYSIS. 


97 


-**. 

-£S*-  t   -0 

etrtrJfe  .     rJ*f- 


k*" 


•      ~"\iger  (calmato) 


!   -*-  -•-          (i 

*T*      «- 


:    0    0 
0 


»    4 

—  *»- 
f 

.VI  : 


? 


« 


^7^1""  I21j^  -~^U  -]] 


•O- 

t: 
"£>' 


1)8 


HA  RMOM  C  ANA  L  YS/S. 


Ibid.     ,  - 

^         (5*  •  I   s»      ^  . 


*1iH 


i=tz  -  IJ=^=:- 


146.     ^  //<?<7ro. 


animate 


J.  lixri-1,  Violin  Sonata. 


».•  ...     • 

5&-'      -^^ 


:±q  :;  li 

- -q.->  q*  •::}.•- 

^     5    ^ 
|^-      ^     ^ 


=t     "3=*"   =t 
•*•     83: 


-4- 1  ^  3  -\  [~--3~-^-,~-----~+-^i 

>-4-*-^-.J-  r*""-=rJf*--T  •  ^-^ 


-t    =t     3- 
3    *   JF 


: 
^ 


-H--  ---;+ 
--g;     V  &<> 


1 


//  I IIMONIC  ANAL  }'.>/,•> . 


pz^z:  ^=^ 


fe 


-1- 

I 


3*=* 


„: 

S-» • 

^=1: 


147.     Allegro  non  troppo.  KIMSKY-KORSAKOFF,  Schchorazaile. 


100 


HA RMONI C  ANAL  YSIS. 


m 


^L     — iit-J 


—M — Li — I — -r^ — ^"x — 5 — *~SJ 

— '5^-r —        • — 

-&-• 


3&= 


>—?= 

-|— 1— *-*=: 


-fcfcr 


— L 


_  -b+—t 

'— Si^t 


V-g 


^i^ 


HA  KM  OX/  <:   A  XA  A  1  'HIS. 


101 


-*  I   ^g~ — 


r 

r=g?*:j 


/r 


-<S~'  -&- 

SEEE^Eiiz 


J3*1- 


iS!— 

t 


«— B  o-          ----*— S-i*»' 

:ig-^~^-^-p=^: 


|t%£i=    zz^srzL-JjEfq 


:3 


-•-  -»- 
*— ±-*-i    -•- 

^"i=i 


J>    -•- 

-£=1=— F — i-h- 


Si 


fl 


^^E 


|2^SE3E 


E2!F=^fl 

«jir  =SH 


CHOPIN,  Prelude 


102 


HA  RMOMC  A  NA  L  YSIS. 


— >  -- - 

^     V  ^T"-*1'^-  -I- 


-*+&—  _* 4-—X0- 

fe7-^        -^ix—r—         — g  •— •— 


— n- 


1 0 


-&*—*- 
- » • 
-#-p — «- 


>-• 


:  r5-^--^=t 

j±d2=       =^a=a: 

-=S3r 


=*^^ 

^ 


t?=3=n 

tEE(=rE 


149.     Atnliinti   maestoso. 


\VA<;NKU,  Tannlmuscr. 


"*  "    A 


I 


11 A  RM 0\l  C  ANA  L  YSIS. 


103 


150.     A  dagio. 
8va. 


WAGNER,  Lohengrin. 

IX 


- 


B  C"       -  " ^  -w-"r   m-* 


/S1  I 


-       ^  -      H          -4»  O 

^  r.>.=      _l^5.= 

•*  r         i     r 


104  HARMONIC  ANALYSIS. 

151.     Molto  moderalo.  WAGNEK,  Tristan. 


^^    I         I         I   .     I—, 


i     r£Li 

_£z=2t=       —  g- 


v-r»  ^- — 


I 


_?i^^rJ 


HARMONIC  ANALYSIS. 


105 


r  s 


tpV;;  :-. 


106 


HA  RMONIC  A  AM  L  VN/.S'. 


*     II 


HA  KM  ONI  C  A  NA  L  YSIS. 


107 


L — =fc 


—      is* — | 


-«-       V. 


-**  -sttj^^—.- 


d- 


r 


=f£?^feJ 


: 


- 


5*         «- 


b,          b 

^  !       J 


m 


II 


^-^^^^^^^^^-  7"^ — ~  |        -^  *        -»  . 

1zi>£;^  *?§:::    •    . 
?*=  =^fSjgj£j^p  1  ^1^3 


108  HARMONIC  ANALYSIS. 

152.      7Ve*  lent.  D'!NDV,  Mcdee. 


-3-x- 


fc=  ^pr<3=         =3 — I—  T3~          =3J 

r  >>  *  >i/ 


b£  •  ~^~  -F^^^^b^p^- 


^S^ 

r^P- 


Ft/. 


vzz  -  -X-3) | iz^d 


HA  KM  ONI  C  A  NA  L  YXIS. 


109 


®zr. 


? 


' 


J2.£2-  •          «x=-  • 

Erg:.     OK.. 

fr^-"-     «  "T-J_ 


W&- 


W 


S 


110 


HARMONIC  ANALYSIS. 


E:: 


ft*          ftj.       Jg. 


=t=: 


153.     Appassionato, 


GLAZOUNOFF,  Valse. 


f 


4 


8ra. 


HARMONIC  ANALYSIS.  Ill 

Section  60.  Conclusion.  The  difficulty  in  preparing  this 
book  was  not  what  to  use,  but  what  not  to  use.  To  those  who  care 
to  go  farther  and  to  investigate  in  a  broad  and  general  way,  the 
author  would  recommend  the  best  of  Schubert's  Songs,  Schumann's 
Davidsbundler,  the  Kreisleriana,  and  the  great  C  major  Fantaisie, 
Chopin's  Etudes  (possibly),  the  Brahms  Variations,  Wagner's  Die 
Walkure  (put  off  examination  of  the  other  things  until  a  more 
general  view  of  modern  harmonics  has  been  taken),  the  short  Piano 
Pieces  and  the  Songs  of  the  two  racially  different  harmonists,  Grieg 
and  Tschaikowsky,  the  Beatitudes  of  Cdsar  Franck,  and  his  great 
Piano  Pieces,  returning  again  and  again  to  the  Beethoven  of  the 
Piano  Sonatas  and  of  the  greater  Variations.  A'erdi  in  his  latest 
works  —  Othello,  Fal staff,  the  Requiem  —  and  Puccini  in  Ln  Tosca, 
will  display  the  new  Italian  school  at  its  best,  and  the  Extremists 
of  the  Puissian  piano  writers  —  Glazounoff,  for  instance — will  lie 
found  well  worth  the  while.  The  chamber  music  of  such  radically 
diverse  minds  as  Sinding  the  Norseman,  and  that  man  of  the  South, 
Goldmark,  will,  when  studied  and  compared,  give  food  for  thought 
and  criticism. 

The  investigating  student  will  also  find  both  startling  and 
exquisite  things  in  the  works  of  not  a  few  Americans,  and  he  may 
draw  profit  from  the  Bohemian  Dvorak,  especially  from  his  fine 
Requiem  and  from  his  Piano  Trios.  He  may  also  learn  that  the 
new-Germans  have  said  little  of  originality  in  a  harmonic  way  ; 
that  Richard  Strauss,  for  example,  although  he  has  gone  far,  has  in 
many  of  his  works  given  more  color  and  counterpoint  than  harmony  ; 
he  may  find  out  that  to  go  to  the  apparent  End  of  Things  in  Har- 
mony —  tli at  is,  what  we  would  call  the  End  —  lie  must  go  to  the 
out  and  out  Cacophanists,  to  the  Frenchmen  of  this  day,  to  P'lndy, 
to  Bruneau,  for  instance,  and  to  those  occasional  Americans  who 
follow  the  same  tendency. 


APPENDIX. 

TEN   FRAGMENTS  OF   VARIOUS  NATURES,  CAREFULLY 
ANALYZED   AND    DISCUSSED. 


SCHUMANN,  ( >p.  68. 


:*=£^d 


C  I 


V.       I    GI6       Va 


A.    Principle  No.  8:  tlie  impression  is  that  of  a  change  of  key  followed 
by  a  deceptive  resolution. 


B     Too  short  for  a  modulation 

C.  Some  would  call  iliis  A  minor. 

D.  "The  identity  of  a  chord  dependson  its  resolution  :  "   Principle  No.  ;i. 
Apply  also  Principle  No.  ~>. 


114 


II A  RM  ONI  C  A  NA  L  YSIS. 


z&i^iEjA 


N^ 


m^^j 


^^  =ii 

-?    0.   — fc»H 


J6       IV  T6  eVI17o        E 

4 

E.    See  Principle  No.  12. 


BfeV, 


__    --^ 

ES   s:*r**£«-^ 


F.    Unmistakably  I     in   C:   especially  as  it    is  preceded  b^  an  altered  n  . 

o 

4 

The  preceding  measure   may   be   called   C  major,    for  the    impression   of  the 
V  chord  i-  that  of  unrest,  \\hieh   is  never  the  impression  of  a  tonic.      Still  on 

account   of  the  duration  of  the  apparent   V     some  analyx.e  this   measure  as: 

F,  V  ,  I.      We   regard   it    as  but  a  step  in  the  movement  toward    the    I  at 

5  4 

letter   F. 


HA  RMONI C  A  NA  L  YSIS. 


115 


m i 1 — ~*  y — 

*^^]  *-•— j=|  || 


D.  O  .P. 


G.  The  old-fashioned  marking  would  read:  d  V  ,  G  V  ;  and  the  GSof 
the  preceding  measure  would  probably  be  called  a  passing  tone.  The  impres- 
sions are  certainly  those  of  dominants,  but  whether  ttpparent  or  real,  the 
listener  must  decide.  We  call  them  apparent  dominants,  and  stay  in  C. 


2.     Allegro  brillante. 


+      D.App 


VERDI,  Falstaff. 


<;.  i. 


1 


i 


I).  Ap 


lib 


HA  RMOX1 C  A  NA  L  1'SVS. 


3.     Allegro  con  brio. 


MENDKI.SSOHN,  Fugue. 


:v  c 


tr 


E       +          E        4-          E        +  o 


App. 


V 


1 


App. 


App. 


App. 


. 


"6 
['3] 


V.          I. 


F  V. 


HARMONIC  AXALYS1.1. 


117 


•  MP-S- 
2R 


.. . 

s 


I         vi    Cn 


App. 


App. 


V  O     V2   I6  F.V        I  BbV2    i6cu 


E  -f-  E  +  K  + 


252  

— 

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4^-7*  tp^^    ' 

* 

fm\'    n         1                                                               ' 

' 

[<•>•,  y                                    m 

I 

**Sh       HJ                             r 

i  i 
i 


4.     Rapido.    Prestissimo. 
App.  App. 


LISZT,  Rhapsody. 


4- U 


FIV7 
rfii-i 


118 


HARMONIC  ANALYSIS. 


This  characteristic  passage  is  built  wholly  on  one  chord,  the  two  upper 
members  in  each  quarter  count  being  preceded  by  appoggiaturas.  It  is 
hardly  worth  while  to  figure  each  inversion. 


5.    Molto  agitato. 

K 


F.A.  A  pp. 


CHOPIN,  Prelude  No.  8. 
K  F.A.  A  pp. 


A.  Tlie  root  ]>rogression,  n  V  .  is  stronger,  hence  better,  than  vn°  V  ; 
furthennore  the  context— see  measure  3  —  shows  unmistakably  that  the 
harmonic  motive  is  11"  V  ,  and  nothing  else. 


///]  HMOM  C   A  \A  I.  YSIS. 


119 


App. 


*-t  S      \.J 

*       ._ft^_*_ 


c*i.°  V7          bn°  V,        f*vi.«o vn«          V, 

3  3  2 

Knharm.  Notatiou. 

B.  Enharmonic  notation  of  e$  y*  b$  d1>,  the  third,  fifth,  and  seventh  of 
which  are  passing  notes  moving  down  to  gt,  b,  d,  witheJ,  forming  a  cliord  of 
the  reigning  key.  Tlie  notation  in  Hats  simplifies  possibly  for  the  eye,  but  is 
illogical;  for  no  one  hearing  this  piece  and  knowing  it  to  be  in  sharps  would 
ever  imagine,  naturally,  one  single  chord  in  Hats. 


F.A.  A  pp. 


F.A. 


'~*f    •   •     *-»-i~  jj»~- !•'"•-     *— •  "     ,     r-  **      "•— - 
"     >-      ~-  •  4:_-  —  -ir*.  |   *f  '  ^z—F1- 


Enh.  Not. 


C.    To  call  this  chord,  according  to  its  appearance,  the  vn"0  of  A-,  major 
or  minor,  is  to  break  the  sequence,  which  is  unwarrantable.      Tin.-  sequence 


120 


HARMONIC  A NA L  YSIS. 


moves  down  regularly  by  minor  seconds,  and  at  its  end  is  varied  and  made 
more  interesting  by  the  suspension  in  the  buss  ;  this  prolongation  of  the  chord 
also  forms  a  quasi  halting  place  and  makes  more  impressive  the  change  at 

D.    A  dominant  seventh,  by  enharmonic  transformation  of  its  seventh,  or 
of  its  seventh  and  root,  may  become  an  6+  or  a.*4"    modulating  in  the  first 

3 

case  to  the  minor  tonic  a  minor  second  lower,  in  the  second  case  to  a  major 
tonic  a  minor  second  lower  ;  thus  :  from  C'b  to  B&,  minor  or  major.  The 
enharmonics  in  this  present  case  are  Jfe  fb,  for  c$  e.  This  harmonic  subtlety 
was  very  dear  to  Chopin.  See  Section  43. 


Ant.        Ant.      Ant. 


E.  The  soprano  presents  a  subtlety.  Bbb  sounds  A.  The  main  notes  of 
the  soprano,  then,  are  B&  A  A^  G,  and  the  B&  is  used  to  present  to  the  eye 
a  figure  like  that  of  the  first  count. 


BbV,  i  gV7  i  EbV7 


6.     Allegro  maestoso. 

Broken 
App.          Passing  Tones.          ditto 

+ 


HARMONIC  ANALYSIS.  121 

CHOPIN,  Polonaise. 


E        o     +     o     -f    D.  App.  4-          I).  App.     o 


I).  App.  App.          D.  App.      I).  App.       I). 


App.  App.     A]>p.     App.    App.     App.    App.  Apj>.    App.  App. 


Passing  Brokon  Tliinls. 


1 


122 


HARMONIC  ANALYSIS. 


11 

1 

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,                      .        L 

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V7                    BI 

T,  Fugue  on  the  name  of  Bacli. 


App. 


S          O 


f.vfi  V     V2 


App 


1     f:  gV  ,  W 

•-     --— »  'r-S — »—  3T— 


£==*= 


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\  V11'6  «V6  a    VII7°y 


3 


HARMONIC  A NA  L  YSIS. 


123 


c  V 


It  is  impossible  to  hold  any  key  for  any  length  of  time  in  this  example. 
The  impressions  of  key  change  constantly,  and  the  figuring  represents  what 
the  ear  hears,  and  any  attempt  to  use  chromatically  altered  chords  instead  of 
shifting  tonalities  leads  one  into  illogical  markings,  as  the  writer  found  on 
experimenting.  A  reduction  will  soften  certain  harsh  measures  ;  Xos.  3,  4,  5, 
and  6,  on  this  page,  become  not  only  clear,  but  fairly  bland,  when  the  synco- 
pations are  omitted. 


124 


HARMONIC  ANALYSIS. 


App. 


g  »  T  VII 


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aiT 


i^tfca 
^__ 


vii  vii 

3 


r 

o  o  ••         o  o 

cvn4      CVII6         «VII  vn 

a  B  3 

gD.O.P  ...... 


App. 


»- 


•  ? 

££_ 


O  O  OOiOO  OTT 

g  VII  VII  C  VII  VII  Q  VII  VII  g  II  V 


HARMONIC  ANALYSIS. 


125 


8.     .-1  Uegro. 


BACH-TAUSIO. 


JL/.  i    .t  — 

—  _  — 

A 

U^-li-3^3 

* 

. 

—  s?1  —  " 

—  J 

i 

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A.  Passages  composed  of  rapid  and  constant  alternations  of  tonic  and 
dominant,  as  is  this,  may  best  be  analyzed  by  judging  of  the  general  impres- 
sion rather  than  by  naming  each  chord,  a  procedure  which  does  not  agree 
with  what  one  hears. 


1 


-12- 


dn 


126 


HARMONIC  ANALYSIS. 


App.  Chd. 


Ibid. 


B.  This  whole  sequential  strain  passes  so  quickly  by  the  ear  and  has  in  it 
so  much  of  the  F  major  character  —  that  is,  so  many  B  flats  and  E's  —  that 
an  Extremist  would  call  it  throughout,  F  major.  We  prefer  to  regard  it  as 
modulatory  in  nature,  as  it  seems  to  move  up  by  hitches,  and  because  of  the 
"  sham  keys"  which  seem  to  accentuate  the  idea  of  key  change,  being  used 
for  the  sake  of  variety  (see  Section  50,  The  Sequence).  It  is  a  place  very 
difficult  to  mark,  however  one  may  regard  it,  and  we  have  chosen  it  because 
typical  of  countless  Bach  passages.  The  first  sixteenth  note  on  each  eighth 
is  a  chord;  the  other  sixteenth  notes  are  accidental  tone  formations,  contain- 
ing Free  Tones,  Free  Anticipations,  etc.  It  will  be  realized  by  any  one  who 
studies  these  measures  attentively  that  here,  in  "  old  Bach,"  are  distortions 
of  the  key  nearly  if  not  quite  as  great  as  those  practised  to-day  by  the  Out- 
and-Outers. 

App.  Chd.  App.  Chd. 


HARMONIC  ANALYSIS. 


127 


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128 


HARMONIC  ANALYSIS. 


F  V. 


9.     Moderato. 


•f§ 


i4 


¥W 


Ant. 


WAGNER,  Parsival. 


«=?• 


it: 


m 


Ant. 


fjfi  di 


HARMONIC  ANALYSIS. 


129 


F.T. 


10.     Lento  e  maestoso. 


WAGNER,  Parsival. 

S  S  E         E 


di 


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App.        O 


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130 


HA  RM  ONI  C  A  NA  L  YSIS. 


+      o 


A.  A  characteristic  Wagnerian  rising  sequence,  defined  by  the  essential 
chords  on  the  second  and  fourth  beats  in  measures  5,  G,  7.  The  tone  combi- 
nations on  the  first  and  third  beats  of  these  measures  offer  difficulty,  and  only 
recourse  to  enharmonics  will  solve  the  complicated  problem.  The  chord  at  B 
is,  in  reality,  d$  ft  a  c ;  and  at  C,  el  <fi  by,  d.  This  interpretation  gives  two 
chords  in  a  key  —  see  Principle  Xo.  5  —  and  explains  the  inconsistent  and 
mind-disturbing  notation  of  a  passage  which  to  the  ear  is  very  consistent, 
coherent,  and  agreeable.  Numberless  cases  of  this  sort  occur  in  modern  music 
which  may  be  explained  only  in  the  above  way.  The  composer  hears  the  chord 
mentally  and  employs  any  notation  which  seems  to  him  good;  to  the  analyst 
falls  the  task  of  finding  the  needful  enharmonics  and  of  making  them  clear  to 
his  mind. 


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